merge mzuenni changes

21 files changed, 273 insertions, 325 deletions

diff --git a/content/math/divSum.cpp b/content/math/divSum.cpp
new file mode 100644
index 0000000..48302b5
--- /dev/null
+++ b/content/math/divSum.cpp
@@ -0,0 +1,8 @@
+ll divSum(ll n, ll m, ll a, ll b){
+	if (m == 0) return 0;
+	ll ans = a/m * n*(n-1)/2 + b/m * n;
+	a %= m;
+	b %= m;
+	ll y = (a*(n-1)+b) / m;
+	return ans + y * (n-1) - divSum(y, a, m, m-b-1);
+}
diff --git a/content/math/gauss.cpp b/content/math/gauss.cpp
index 8129fd2..d431e52 100644
--- a/content/math/gauss.cpp
+++ b/content/math/gauss.cpp
@@ -14,19 +14,17 @@ void takeAll(int n, int line) {
 int gauss(int n) {
 	vector<bool> done(n, false);
 	for (int i = 0; i < n; i++) {
-		int swappee = i; // Sucht Pivotzeile für bessere Stabilität.
-		for (int j = 0; j < n; j++) {
-			if (done[j]) continue;
-			if (abs(mat[j][i]) > abs(mat[i][i])) swappee = j;
+		int j = i; // Sucht Pivotzeile für bessere Stabilität.
+		for (int k = 0; k < n; k++) {
+			if (!done[k] && abs(mat[k][i]) > abs(mat[i][i])) j = k;
 		}
-		swap(mat[i], mat[swappee]);
+		swap(mat[i], mat[j]);
 		if (abs(mat[i][i]) > EPS) {
 			normalLine(i);
 			takeAll(n, i);
 			done[i] = true;	
 	}}
-	// Ab jetzt nur checks bzgl. Eindeutigkeit/Existenz der Lösung.
-	for (int i = 0; i < n; i++) {
+	for (int i = 0; i < n; i++) { // gauss fertig, prüfe Lösung
 		bool allZero = true;
 		for (int j = i; j < n; j++) allZero &= abs(mat[i][j]) <= EPS;
 		if (allZero && abs(mat[i][n]) > EPS) return INCONSISTENT;
diff --git a/content/math/lgsFp.cpp b/content/math/lgsFp.cpp
index 0241742..bf18c86 100644
--- a/content/math/lgsFp.cpp
+++ b/content/math/lgsFp.cpp
@@ -22,5 +22,4 @@ void gauss(int n, ll mod) {
 		normalLine(i, mod);
 		takeAll(n, i, mod);
 		done[i] = true;
-}}
-// für Eindeutigkeit, Existenz etc. siehe LGS über R @\sourceref{math/gauss.cpp}@
+}} // für Eindeutigkeit, Existenz etc. siehe LGS über R @\sourceref{math/gauss.cpp}@
diff --git a/content/math/linearRecurrence.cpp b/content/math/linearRecurrence.cpp
index 2501e64..a8adacd 100644
--- a/content/math/linearRecurrence.cpp
+++ b/content/math/linearRecurrence.cpp
@@ -1,33 +1,30 @@
-constexpr ll mod = 1'000'000'007;
-vector<ll> modMul(const vector<ll>& a, const vector<ll>& b,
-                  const vector<ll>& c) {
-	ll n = sz(c);
-	vector<ll> res(n * 2 + 1);
-	for (int i = 0; i <= n; i++) { //a*b
-		for (int j = 0; j <= n; j++) {
-			res[i + j] += a[i] * b[j];
-			res[i + j] %= mod;
+constexpr ll mod = 998244353;
+// oder ntt mul @\sourceref{math/transforms/ntt.cpp}@
+vector<ll> mul(const vector<ll>& a, const vector<ll>& b) {
+	vector<ll> c(sz(a) + sz(b) - 1);
+	for (int i = 0; i < sz(a); i++) {
+		for (int j = 0; j < sz(b); j++) {
+			c[i+j] += a[i]*b[j] % mod;
 	}}
-	for (int i = 2 * n; i > n; i--) { //res%c
-		for (int j = 0; j < n; j++) {
-			res[i - 1 - j] += res[i] * c[j];
-			res[i - 1 - j] %= mod;
-	}}
-	res.resize(n + 1);
-	return res;
+	for (ll& x : c) x %= mod;
+	return c;
 }
 
 ll kthTerm(const vector<ll>& f, const vector<ll>& c, ll k) {
-	assert(sz(f) == sz(c));
-	vector<ll> tmp(sz(c) + 1), a(sz(c) + 1);
-	tmp[0] = a[1] = 1; //tmp = (x^k) % c
-
-	for (k++; k > 0; k /= 2) {
-		if (k & 1) tmp = modMul(tmp, a, c);
-		a = modMul(a, a, c);
-	}
-
-	ll res = 0;
-	for (int i = 0; i < sz(c); i++) res += (tmp[i+1] * f[i]) % mod;
-	return res % mod;
+	int n = sz(c);
+	vector<ll> q(n + 1, 1);
+	for (int i = 0; i < n; i++) q[i + 1] = (mod - c[i]) % mod;
+	vector<ll> p = mul(f, q);
+	p.resize(n);
+	p.push_back(0);
+	do {
+		vector<ll> q2 = q;
+		for (int i = 1; i <= n; i += 2) q2[i] = (mod - q2[i]) % mod;
+		vector<ll> x = mul(p, q2), y = mul(q, q2);
+		for (int i = 0; i <= n; i++){
+			p[i] = i == n ? 0 : x[2*i + (k&1)];
+			q[i] = y[2*i];
+		}
+	} while (k /= 2);
+	return p[0];
 }
diff --git a/content/math/linearRecurrenceOld.cpp b/content/math/linearRecurrenceOld.cpp
new file mode 100644
index 0000000..2501e64
--- /dev/null
+++ b/content/math/linearRecurrenceOld.cpp
@@ -0,0 +1,33 @@
+constexpr ll mod = 1'000'000'007;
+vector<ll> modMul(const vector<ll>& a, const vector<ll>& b,
+                  const vector<ll>& c) {
+	ll n = sz(c);
+	vector<ll> res(n * 2 + 1);
+	for (int i = 0; i <= n; i++) { //a*b
+		for (int j = 0; j <= n; j++) {
+			res[i + j] += a[i] * b[j];
+			res[i + j] %= mod;
+	}}
+	for (int i = 2 * n; i > n; i--) { //res%c
+		for (int j = 0; j < n; j++) {
+			res[i - 1 - j] += res[i] * c[j];
+			res[i - 1 - j] %= mod;
+	}}
+	res.resize(n + 1);
+	return res;
+}
+
+ll kthTerm(const vector<ll>& f, const vector<ll>& c, ll k) {
+	assert(sz(f) == sz(c));
+	vector<ll> tmp(sz(c) + 1), a(sz(c) + 1);
+	tmp[0] = a[1] = 1; //tmp = (x^k) % c
+
+	for (k++; k > 0; k /= 2) {
+		if (k & 1) tmp = modMul(tmp, a, c);
+		a = modMul(a, a, c);
+	}
+
+	ll res = 0;
+	for (int i = 0; i < sz(c); i++) res += (tmp[i+1] * f[i]) % mod;
+	return res % mod;
+}
diff --git a/content/math/math.tex b/content/math/math.tex
index f670a70..644fbc8 100644
--- a/content/math/math.tex
+++ b/content/math/math.tex
@@ -109,8 +109,6 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch:
 	\sourcecode{math/millerRabin.cpp}

 	\method{rho}{findet zufälligen Teiler}{\sqrt[\leftroot{3}\uproot{2}4]{n}}

 	\sourcecode{math/rho.cpp}

-	%\method{squfof}{findet zufälligen Teiler}{\sqrt[\leftroot{4}\uproot{2}4]{n}}

-	%\sourcecode{math/squfof.cpp}

 \end{algorithm}

 

 \begin{algorithm}{Teiler}

@@ -138,8 +136,9 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch:
 	Sei $f(n)=c_{0}f(n-1)+c_{1}f(n-2)+\dots + c_{n-1}f(0)$ eine lineare Rekurrenz.

 	

 	\begin{methods}

-		\method{kthTerm}{Berechnet $k$-ten Term einer Rekurrenz $n$-ter Ordnung}{\log(k)\cdot n^2}

+		\method{kthTerm}{Berechnet $k$-ten Term einer Rekurrenz $n$-ter Ordnung}{\log(k)\cdot \text{mul}(n)}

 	\end{methods}

+	Die Polynom-Multiplikation kann auch mit NTT gemacht werden!

 	\sourcecode{math/linearRecurrence.cpp}

 	Alternativ kann der \mbox{$k$-te} Term in \runtime{n^3\log(k)} berechnet werden:

 	$$\renewcommand\arraystretch{1.5}

@@ -308,7 +307,10 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch:
 \method{gauss}{löst LGS}{n^3}

 \sourcecode{math/gauss.cpp}

 

-\vfill\null\columnbreak

+\begin{algorithm}{Inversionszahl}

+	\vspace{-2pt}

+	\sourcecode{math/inversions.cpp}

+\end{algorithm}

 

 \begin{algorithm}{Numerisch Extremstelle bestimmen}

 	\sourcecode{math/goldenSectionSearch.cpp}

@@ -318,7 +320,6 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch:
 	\sourcecode{math/simpson.cpp}

 \end{algorithm}

 

-

 \begin{algorithm}{Polynome, FFT, NTT \& andere Transformationen}

 	Multipliziert Polynome $A$ und $B$.

 	\begin{itemize}

@@ -342,21 +343,6 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch:
     \sourcecode{math/transforms/seriesOperations.cpp}

 \end{algorithm}

 

-\begin{algorithm}{Inversionszahl}

-	\sourcecode{math/inversions.cpp}

-\end{algorithm}

-

-\subsection{Satz von \textsc{Sprague-Grundy}}

-Weise jedem Zustand $X$ wie folgt eine \textsc{Grundy}-Zahl $g\left(X\right)$ zu:

-\[

-g\left(X\right) := \min\left\{

-\mathbb{Z}_0^+ \setminus

-\left\{g\left(Y\right) \mid Y \text{ von } X \text{ aus direkt erreichbar}\right\}

-\right\}

-\]

-$X$ ist genau dann gewonnen, wenn $g\left(X\right) > 0$ ist.\\

-Wenn man $k$ Spiele in den Zuständen $X_1, \ldots, X_k$ hat, dann ist die \textsc{Grundy}-Zahl des Gesamtzustandes $g\left(X_1\right) \oplus \ldots \oplus g\left(X_k\right)$.

-

 \subsection{Kombinatorik}

 

 \paragraph{\textsc{Wilson}'s Theorem}

@@ -389,7 +375,9 @@ so gilt
 %\begin{algorithm}{Binomialkoeffizienten}

 \paragraph{Binomialkoeffizienten}

 	Die Anzahl der \mbox{$k$-elementigen} Teilmengen einer \mbox{$n$-elementigen} Menge.

-

+	

+	\input{math/tables/binom}

+	

 	\begin{methods}

 		\method{precalc}{berechnet $n!$ und $n!^{-1}$ vor}{\mathit{lim}}

 		\method{calc\_binom}{berechnet Binomialkoeffizient}{1}

@@ -498,7 +486,7 @@ Die Anzahl der Partitionen von $n$ mit Elementen aus ${1,\dots,k}$.
 \begin{align*}

 	p_0(0)=1 \qquad p_k(n)&=0 \text{ für } k > n \text{ oder } n \leq 0 \text{ oder } k \leq 0\\

 	p_k(n)&= p_k(n-k) + p_{k-1}(n-1)\\[2pt]

-	p(n)&=\sum_{k=1}^{n} p_k(n)=p_n(2n)=\sum\limits_{k\neq0}^\infty(-1)^{k+1}p\bigg(n - \frac{k(3k-1)}{2}\bigg)

+	p(n)=\sum_{k=1}^{n} p_k(n)&=p_n(2n)=\sum\limits_{k=1}^\infty(-1)^{k+1}\bigg[p\bigg(n - \frac{k(3k-1)}{2}\bigg) + p\bigg(n - \frac{k(3k+1)}{2}\bigg)\bigg]

 \end{align*}

 \begin{itemize}

 	\item in Formel $3$ kann abgebrochen werden wenn $\frac{k(3k-1)}{2} > n$.

@@ -508,6 +496,59 @@ Die Anzahl der Partitionen von $n$ mit Elementen aus ${1,\dots,k}$.
 \subsection{The Twelvefold Way \textnormal{(verteile $n$ Bälle auf $k$ Boxen)}}

 \input{math/tables/twelvefold}

 

+\subsection{Platonische Körper}

+\input{math/tables/platonic}

+

+\input{math/tables/probability}

+

+\subsection{Satz von \textsc{Sprague-Grundy}}

+Weise jedem Zustand $X$ wie folgt eine \textsc{Grundy}-Zahl $g\left(X\right)$ zu:

+\[

+g\left(X\right) := \min\left\{

+\mathbb{Z}_0^+ \setminus

+\left\{g\left(Y\right) \mid Y \text{ von } X \text{ aus direkt erreichbar}\right\}

+\right\}

+\]

+$X$ ist genau dann gewonnen, wenn $g\left(X\right) > 0$ ist.\\

+Wenn man $k$ Spiele in den Zuständen $X_1, \ldots, X_k$ hat, dann ist die \textsc{Grundy}-Zahl des Gesamtzustandes $g\left(X_1\right) \oplus \ldots \oplus g\left(X_k\right)$.

+

+\subsection{Nim-Spiele}

+\begin{itemize}

+	\item[\ding{182}] letzter gewinnt (normal)

+	\item[\ding{183}] letzter verliert

+\end{itemize}

+\input{math/tables/nim}

+

+\subsection{Verschiedenes}

+\input{math/tables/stuff}

+

+\begin{algorithm}{Div Sum}

+	\method{divSum}{berechnet $\sum_{i=0}^{n-1} \left\lfloor \frac{a\cdot i + b}{m}  \right\rfloor$}{\log(n)}

+	\textbf{Wichtig:} $b$ darf nicht negativ sein!

+	\sourcecode{math/divSum.cpp}

+\end{algorithm}

+

+\begin{algorithm}{Min Mod}

+	\begin{methods}

+		\method{firstVal}{berechnet den ersten Wert von $0,\ a, \ldots,\ a \cdot i \bmod{m}$,}{\log(m)}

+		\method{}{der in $[l, r]$ liegt. Gibt $-1$ zurück, falls er nicht existiert.}{}

+		\method{minMod}{berechnet das Minimum von $(a \cdot i + b) \bmod{m}$ für $i \in [0, n)$}{\log(m)}

+	\end{methods}

+	\textbf{Wichtig:} $0 \leq a, b, l, r < m$

+	\sourcecode{math/minMod.cpp}

+\end{algorithm}

+

+\subsection{Reihen}

+\input{math/tables/series}

+

+\subsection{Wichtige Zahlen}

+\input{math/tables/prime-composite}

+

+\subsection{Recover $\boldsymbol{x}$ and $\boldsymbol{y}$ from $\boldsymbol{y}$ from $\boldsymbol{x\*y^{-1}}$ }

+\method{recover}{findet $x$ und $y$ für $x=x\*y^{-1}\bmod m$}{\log(m)}

+\textbf{WICHTIG:} $x$ und $y$ müssen kleiner als $\sqrt{\nicefrac{m}{2}}$ sein!

+\sourcecode{math/recover.cpp}

+

 \optional{

 \subsection{Primzahlzählfunktion $\boldsymbol{\pi}$}

 \begin{methods}

@@ -516,9 +557,10 @@ Die Anzahl der Partitionen von $n$ mit Elementen aus ${1,\dots,k}$.
 	\method{pi}{zählt Primzahlen  $\leq n$ ($n < N^2$)}{n^{2/3}}

 \end{methods}

 \sourcecode{math/piLehmer.cpp}

-}

 

-%\input{math/tables/numbers}

+\subsection{Primzahlzählfunktion $\boldsymbol{\pi}$}

+\sourcecode{math/piLegendre.cpp}

+}

 

 \begin{algorithm}[optional]{Big Integers}

 	\sourcecode{math/bigint.cpp}

diff --git a/content/math/minMod.cpp b/content/math/minMod.cpp
new file mode 100644
index 0000000..a80e783
--- /dev/null
+++ b/content/math/minMod.cpp
@@ -0,0 +1,22 @@
+ll firstVal(ll a, ll m, ll l, ll r) {
+	if (l == 0) return 0;
+	if (a == 0) return -1;
+	if ((l-1)/a < r/a) return (l+a-1) / a*a;
+	ll s = (r+a-1) / a*a;
+	ll v = firstVal(m % a, a, s-r, s-l);
+	return v < 0 ? -1 : s - v;
+}
+
+ll minMod(ll n, ll m, ll a, ll b) {
+	if (a == 0) return b;
+	ll g = gcd(m, a);
+	ll c = b % g;
+	m /= g;
+	a /= g;
+	b /= g;
+	ll ai = multInv(a, m);
+	ll l = ai*b % m;
+	ll r = (n-1 + ai*b) % m;
+	if (n >= m || l > r) return c;
+	return a * firstVal(ai, m, l, r) % m * g + c;
+}
\ No newline at end of file
diff --git a/content/math/polynomial.cpp b/content/math/polynomial.cpp
index 44f6207..84f3aaa 100644
--- a/content/math/polynomial.cpp
+++ b/content/math/polynomial.cpp
@@ -1,7 +1,7 @@
 struct poly {
 	vector<ll> data;
 
-	poly(int deg = 0) : data(max(1, deg)) {}
+	poly(int deg = 0) : data(1 + deg) {}
 	poly(initializer_list<ll> _data) : data(_data) {}
 
 	int size() const {return sz(data);}
@@ -40,17 +40,18 @@ struct poly {
 
 	//return p(x+a)
 	poly operator<<(ll a) const {
-		poly res(size());
+		poly res(size() - 1);
 		for (int i = size() - 1; i >= 0; i--) {
 			for (int j = size() - i - 1; j >= 1; j--)
 				res[j] = (res[j] * a + res[j - 1]) % mod;
-			res[0] = (res[0] * a + res[i]) % mod;
+			res[0] = (res[0] * a + data[i]) % mod;
 		}
 		return res;
 	}
 
 	pair<poly, poly> divmod(const poly& d) const {
 		int i = size() - d.size();
+		if (i <= 0) return {{}, *this};
 		poly s(i + 1), r = *this;
 		ll inv = multInv(d.data.back(), mod);
 		for (; i >= 0; i--) {
diff --git a/content/math/recover.cpp b/content/math/recover.cpp
new file mode 100644
index 0000000..1a593f0
--- /dev/null
+++ b/content/math/recover.cpp
@@ -0,0 +1,13 @@
+ll sq(ll x) {return x*x;}
+
+array<ll, 2> recover(ll c, ll m) {
+	array<ll, 2> u = {m, 0}, v = {c, 1};
+	while (m <= 2 * sq(v[0])) {
+		ll q = u[0] / v[0];
+		u[0] -= q * v[0];
+		u[1] -= q * v[1];
+		swap(u, v);
+	}
+	if (v[1] <= 0 || 2 * sq(v[1]) >= m) return {-1, -1};
+	return v;
+}
diff --git a/content/math/shortModInv.cpp b/content/math/shortModInv.cpp
index f696cce..cf91ca0 100644
--- a/content/math/shortModInv.cpp
+++ b/content/math/shortModInv.cpp
@@ -1,3 +1,3 @@
 ll multInv(ll x, ll m) { // x^{-1} mod m
-    return 1 < x ? m - multInv(m % x, x) * m / x : 1;
+	return 1 < x ? m - multInv(m % x, x) * m / x : 1;
 }
diff --git a/content/math/squfof.cpp b/content/math/squfof.cpp
deleted file mode 100644
index 1cb97de..0000000
--- a/content/math/squfof.cpp
+++ /dev/null
@@ -1,89 +0,0 @@
-using lll = __int128;

-

-constexpr lll multipliers[] = {1, 3, 5, 7,

-                               11, 3*5, 3*7, 3*11,

-                               5*7, 5*11, 7*11,

-                               3*5*7, 3*5*11, 3*7*11,

-                               5*7*11, 3*5*7*11};

-

-lll root(lll x) {

-	lll r = sqrtl(x);

-	while(r*r < x) r++;

-	while(r*r > x) r--;

-	return r;

-}

-

-lll croot(lll x) {

-	lll r = cbrtl(x);

-	while(r*r*r < x) r++;

-	while(r*r*r > x) r--;

-	return r;

-}

-

-lll squfof(lll N) {

-	lll s = croot(N);

-	if (s*s*s == N) return s;

-	s = root(N);

-	if (s*s == N) return s;

-	for (lll k : multipliers) {

-		lll D = k * N;

-		lll Po, P, Pprev, q, b, r, i;

-		Po = Pprev = P = root(D);

-		lll Qprev = 1;

-		lll Q = D - Po*Po;

-		lll L = 2 * root(2 * s);

-		lll B = 3 * L;

-		for (i = 2; i < B; i++) {

-			b = (Po + P) / Q;

-			P = b*Q - P;

-			q = Q;

-			Q = Qprev + b * (Pprev - P);

-			r = root(Q);

-			if (!(i & 1) && r*r == Q) break;

-			Qprev = q;

-			Pprev = P;

-		}

-		if (i >= B) continue;

-		b = (Po - P) / r;

-		Pprev = P = b*r + P;

-		Qprev = r;

-		Q = (D-Pprev*Pprev)/Qprev;

-		i = 0;

-		do {

-			b = (Po + P) / Q;

-			Pprev = P;

-			P = b*Q - P;

-			q = Q;

-			Q = Qprev +	b * (Pprev - P);

-			Qprev = q;

-			i++;

-		} while(P != Pprev);

-		r = gcd(N, Qprev);

-		if (r != 1 && r != N) return r;

-	}

-	exit(1);//try fallback to pollard rho

-}

-

-constexpr lll trialLim = 5'000;

-

-void factor(lll n, map<lll, int>& facts) {

-	for (lll i = 2; i * i <= n && i <= trialLim; i++) {

-		while (n % i == 0) {

-			facts[i]++;

-			n /= i;

-	}}

-	if (n > 1 && n < trialLim * trialLim) {

-		facts[n]++;

-	} else {

-		vector<lll> todo = {n};

-		while (!todo.empty()) {

-			lll c = todo.back();

-			todo.pop_back();

-			if (c == 1) continue;

-			if (isPrime(c)) {

-				facts[c]++;

-			} else {

-				lll d = squfof(c);

-				todo.push_back(d);

-				todo.push_back(c / d);

-}}}}

diff --git a/content/math/tables.tex b/content/math/tables.tex
deleted file mode 100644
index c422d73..0000000
--- a/content/math/tables.tex
+++ /dev/null
@@ -1,22 +0,0 @@
-\enlargethispage{0.2cm}
-\begin{multicols*}{2}
-	\refstepcounter{subsection}
-	\subsectionmark{Tables}
-	\addcontentsline{toc}{subsection}{\protect\numberline{\thesubsection}Tables}
-
-	\input{math/tables/binom}
-	\vfill
-	\input{math/tables/prime-composite}
-	\vfill
-	\input{math/tables/platonic}
-	\vfill
-	\input{math/tables/series}
-
-	\columnbreak
-
-	\input{math/tables/probability}
-	\vfill
-	\input{math/tables/stuff}
-	\vfill
-	\input{math/tables/nim}
-\end{multicols*}
diff --git a/content/math/tables/binom.tex b/content/math/tables/binom.tex
index 878a6b0..9fc9ae3 100644
--- a/content/math/tables/binom.tex
+++ b/content/math/tables/binom.tex
@@ -1,28 +1,27 @@
-\begin{tabularx}{\linewidth}{|XXXX|}
+\begin{expandtable}
+\begin{tabularx}{\linewidth}{|C|}
 	\hline
-	\multicolumn{4}{|c|}{Binomialkoeffizienten} \\
-	\hline
-	\multicolumn{4}{|c|}{
 	$\frac{n!}{k!(n - k)!} \hfill=\hfill
 	\binom{n}{k} \hfill=\hfill
 	\binom{n}{n - k} \hfill=\hfill
 	\frac{n}{k}\binom{n - 1}{k - 1} \hfill=\hfill
 	\frac{n-k+1}{k}\binom{n}{k - 1} \hfill=\hfill
-	\binom{n - 1}{k} + \binom{n - 1}{k - 1} \hfill=\hfill
+	\frac{k+1}{n-k}\binom{n}{k + 1} \hfill=\hfill$\\
+	
+	$\binom{n - 1}{k - 1} + \binom{n - 1}{k} \hfill=\hfill
+	\binom{n + 1}{k + 1} - \binom{n}{k + 1} \hfill=\hfill
 	(-1)^k \binom{k - n - 1}{k} \hfill\approx\hfill
-	2^{n} \cdot \frac{2}{\sqrt{2\pi n}}\cdot\exp\left(-\frac{2(x - \frac{n}{2})^2}{n}\right)$
-	} \\
+	2^{n} \cdot \frac{2}{\sqrt{2\pi n}}\cdot\exp\left(-\frac{2(x - \frac{n}{2})^2}{n}\right)$\\
 	\grayhline
 	
-	$\sum\limits_{k = 0}^n \binom{n}{k} = 2^n$ &
-	$\sum\limits_{k = 0}^n \binom{k}{m} = \binom{n + 1}{m + 1}$ &
-	$\sum\limits_{i = 0}^n \binom{n}{i}^2 = \binom{2n}{n}$ &
-	$\sum\limits_{k = 0}^n\binom{r + k}{k} = \binom{r + n + 1}{n}$\\
+	$\sum\limits_{k = 0}^n \binom{n}{k} = 2^n\hfill
+	\sum\limits_{k = 0}^n \binom{k}{m} = \binom{n + 1}{m + 1}\hfill
+	\sum\limits_{i = 0}^n \binom{n}{i}^2 = \binom{2n}{n}\hfill
+	\sum\limits_{k = 0}^n\binom{r + k}{k} = \binom{r + n + 1}{n}$\\
 	
-	$\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n - k}{m - k}$ &
-	$\sum\limits_{k = 0}^n \binom{r}{k}\binom{s}{n - k} = \binom{r + s}{n}$ &
-	\multicolumn{2}{l|}{
-	$\sum\limits_{i = 1}^n \binom{n}{i} F_i = F_{2n} \quad F_n = n\text{-th Fib.}$
-	}\\
+	$\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n - k}{m - k}\hfill
+	\sum\limits_{k = 0}^n \binom{r}{k}\binom{s}{n - k} = \binom{r + s}{n}\hfill
+	\sum\limits_{i = 1}^n \binom{n}{i} \mathit{Fib}_i = \mathit{Fib}_{2n}$\\
 	\hline
 \end{tabularx}
+\end{expandtable}
diff --git a/content/math/tables/nim.tex b/content/math/tables/nim.tex
index 8490d42..66e289e 100644
--- a/content/math/tables/nim.tex
+++ b/content/math/tables/nim.tex
@@ -1,7 +1,6 @@
+\begin{expandtable}
 \begin{tabularx}{\linewidth}{|p{0.37\linewidth}|X|}
 	\hline
-	\multicolumn{2}{|c|}{Nim-Spiele (\ding{182} letzter gewinnt (normal), \ding{183} letzter verliert)} \\
-	\hline
 	Beschreibung &
 	Strategie \\
 	\hline
@@ -94,3 +93,5 @@
 	Periode ab $n = 72$ der Länge $12$.\\
 	\hline
 \end{tabularx}
+\end{expandtable}
+	
\ No newline at end of file
diff --git a/content/math/tables/numbers.tex b/content/math/tables/numbers.tex
deleted file mode 100644
index 1dc9f38..0000000
--- a/content/math/tables/numbers.tex
+++ /dev/null
@@ -1,59 +0,0 @@
-\begin{expandtable}
-\begin{tabularx}{\linewidth}{|l|X|}
-	\hline
-	\multicolumn{2}{|c|}{Berühmte Zahlen} \\
-	\hline
-	\textsc{Fibonacci}	&
-	$f(0) = 0 \quad
-	f(1) = 1 \quad
-	f(n+2) = f(n+1) + f(n)$ \\
-	\grayhline
-	
-	\textsc{Catalan}	&
-	$C_0 = 1 \qquad
-	C_n = \sum\limits_{k = 0}^{n - 1} C_kC_{n - 1 - k} =
-	\frac{1}{n + 1}\binom{2n}{n} = \frac{2(2n - 1)}{n+1} \cdot C_{n-1}$ \\
-	\grayhline
-	
-	\textsc{Euler} I &
-	$\eulerI{n}{0} = \eulerI{n}{n-1} = 1 \qquad
-	\eulerI{n}{k} = (k+1) \eulerI{n-1}{k} + (n-k) \eulerI{n-1}{k-1} $ \\
-	\grayhline
-	
-	\textsc{Euler} II &
-	$\eulerII{n}{0} = 1 \quad
-	\eulerII{n}{n} = 0 \quad$\\
-	& $\eulerII{n}{k} = (k+1) \eulerII{n-1}{k} + (2n-k-1) \eulerII{n-1}{k-1}$ \\
-	\grayhline
-	
-	\textsc{Stirling} I &
-	$\stirlingI{0}{0} = 1 \qquad
-	\stirlingI{n}{0} = \stirlingI{0}{n} = 0 \qquad
-	\stirlingI{n}{k} = \stirlingI{n-1}{k-1} + (n-1) \stirlingI{n-1}{k}$ \\
-	\grayhline
-	
-	\textsc{Stirling} II &
-	$\stirlingII{n}{1} = \stirlingII{n}{n} = 1 \qquad
-	\stirlingII{n}{k} = k \stirlingII{n-1}{k} + \stirlingII{n-1}{k-1} =
-	\frac{1}{k!} \sum\limits_{j=0}^{k} (-1)^{k-j}\binom{k}{j}j^n$\\
-	\grayhline
-	
-	\textsc{Bell} &
-	$B_1 = 1 \qquad
-	B_n = \sum\limits_{k = 0}^{n - 1} B_k\binom{n-1}{k}
-	= \sum\limits_{k = 0}^{n}\stirlingII{n}{k}$\\
-	\grayhline
-	
-	\textsc{Partitions} &
-	$p(0,0) = 1 \quad
-	p(n,k) = 0 \text{ für } k > n \text{ oder } n \leq 0 \text{ oder } k \leq 0$ \\
-	& $p(n,k) = p(n-k,k) + p(n-1,k-1)$\\
-	\grayhline
-	
-	\textsc{Partitions} &
-	$f(0) = 1 \quad f(n) = 0~(n < 0)$ \\
-	& $f(n)=\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k+1)}{2})+\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k-1)}{2})$\\
-	
-	\hline
-\end{tabularx}
-\end{expandtable}
diff --git a/content/math/tables/platonic.tex b/content/math/tables/platonic.tex
index f4ee554..2866ccf 100644
--- a/content/math/tables/platonic.tex
+++ b/content/math/tables/platonic.tex
@@ -1,39 +1,39 @@
+\begin{expandtable}
 \begin{tabularx}{\linewidth}{|X|CCCX|}
 	\hline
-	\multicolumn{5}{|c|}{Platonische Körper} \\
-	\hline
-	Übersicht       & Seiten & Ecken & Kanten & dual zu \\
+	Übersicht       & |F|    & |V|   & |E|    & dual zu \\
 	\hline
 	Tetraeder       & 4      & 4     & 6      & Tetraeder \\
-	Würfel/Hexaeder & 6      & 8     & 12     & Oktaeder \\
-	Oktaeder        & 8      & 6     & 12     & Würfel/Hexaeder\\
+	Würfel          & 6      & 8     & 12     & Oktaeder \\
+	Oktaeder        & 8      & 6     & 12     & Würfel\\
 	Dodekaeder      & 12     & 20    & 30     & Ikosaeder \\
 	Ikosaeder       & 20     & 12    & 30     & Dodekaeder \\
 	\hline
 	\multicolumn{5}{|c|}{Färbungen mit maximal $n$ Farben (bis auf Isomorphie)} \\
 	\hline
-	\multicolumn{3}{|l}{Ecken vom Oktaeder/Seiten vom Würfel} &
+	\multicolumn{3}{|l}{|V| vom Oktaeder/|F| vom Würfel} &
 	\multicolumn{2}{l|}{$(n^6 + 3n^4 + 12n^3 + 8n^2)/24$} \\
 
-	\multicolumn{3}{|l}{Ecken vom Würfel/Seiten vom Oktaeder} &
+	\multicolumn{3}{|l}{|V| vom Würfel/|F| vom Oktaeder} &
 	\multicolumn{2}{l|}{$(n^8 + 17n^4 + 6n^2)/24$} \\
 
-	\multicolumn{3}{|l}{Kanten vom Würfel/Oktaeder} &
+	\multicolumn{3}{|l}{|E| vom Würfel/Oktaeder} &
 	\multicolumn{2}{l|}{$(n^{12} + 6n^7 + 3n^6 + 8n^4 + 6n^3)/24$} \\
 
-	\multicolumn{3}{|l}{Ecken/Seiten vom Tetraeder} &
+	\multicolumn{3}{|l}{|V|/|F| vom Tetraeder} &
 	\multicolumn{2}{l|}{$(n^4 + 11n^2)/12$} \\
 
-	\multicolumn{3}{|l}{Kanten vom Tetraeder} &
+	\multicolumn{3}{|l}{|E| vom Tetraeder} &
 	\multicolumn{2}{l|}{$(n^6 + 3n^4 + 8n^2)/12$} \\
 
-	\multicolumn{3}{|l}{Ecken vom Ikosaeder/Seiten vom Dodekaeder} &
+	\multicolumn{3}{|l}{|V| vom Ikosaeder/|F| vom Dodekaeder} &
 	\multicolumn{2}{l|}{$(n^{12} + 15n^6 + 44n^4)/60$} \\
 
-	\multicolumn{3}{|l}{Ecken vom Dodekaeder/Seiten vom Ikosaeder} &
+	\multicolumn{3}{|l}{|V| vom Dodekaeder/|F| vom Ikosaeder} &
 	\multicolumn{2}{l|}{$(n^{20} + 15n^{10} + 20n^8 + 24n^4)/60$} \\
 
-	\multicolumn{3}{|l}{Kanten vom Dodekaeder/Ikosaeder (evtl. falsch)} &
+	\multicolumn{3}{|l}{|E| vom Dodekaeder/Ikosaeder} &
 	\multicolumn{2}{l|}{$(n^{30} + 15n^{16} + 20n^{10} + 24n^6)/60$} \\
 	\hline
 \end{tabularx}
+\end{expandtable}
diff --git a/content/math/tables/prime-composite.tex b/content/math/tables/prime-composite.tex
index 99b3348..073b4ba 100644
--- a/content/math/tables/prime-composite.tex
+++ b/content/math/tables/prime-composite.tex
@@ -1,26 +1,31 @@
-\begin{tabularx}{\linewidth}{|r|r|rIr|rIrIr|C|}
+\begin{expandtable}
+\begin{tabularx}{\linewidth}{|r|rIr|rIr|r|r|}
 	\hline
-	\multicolumn{8}{|c|}{Important Numbers} \\
+	\multirow{2}{*}{$10^x$}
+	       & \multirow{2}{*}{Highly Composite}
+	                                      & \multirow{2}{*}{\# Divs}
+	                                                 & \multicolumn{2}{|c|}{Prime}
+	                                                                         &  \multirow{2}{*}{\# Primes} & \multirow{2}{*}{Primorial} \\
+	       &                              &          &       $<$ &       $>$ &                             &           \\
 	\hline
-	$10^x$ &             Highly Composite &  \# Divs & $<$ Prime & $>$ Prime &                   \# Primes & primorial & \\
-	\hline
-	     1 &                            6 &        4 &      $-3$ &      $+1$ &                           4 &         2 & \\
-	     2 &                           60 &       12 &      $-3$ &      $+1$ &                          25 &         3 & \\
-	     3 &                          840 &       32 &      $-3$ &      $+9$ &                         168 &         4 & \\
-	     4 &                       7\,560 &       64 &     $-27$ &      $+7$ &                      1\,229 &         5 & \\
-	     5 &                      83\,160 &      128 &      $-9$ &      $+3$ &                      9\,592 &         6 & \\
-	     6 &                     720\,720 &      240 &     $-17$ &      $+3$ &                     78\,498 &         7 & \\
-	     7 &                  8\,648\,640 &      448 &      $-9$ &     $+19$ &                    664\,579 &         8 & \\
-	     8 &                 73\,513\,440 &      768 &     $-11$ &      $+7$ &                 5\,761\,455 &         8 & \\
-	     9 &                735\,134\,400 &   1\,344 &     $-63$ &      $+7$ &                50\,847\,534 &         9 & \\
-	    10 &             6\,983\,776\,800 &   2\,304 &     $-33$ &     $+19$ &               455\,052\,511 &        10 & \\
-	    11 &            97\,772\,875\,200 &   4\,032 &     $-23$ &      $+3$ &            4\,118\,054\,813 &        10 & \\
-	    12 &           963\,761\,198\,400 &   6\,720 &     $-11$ &     $+39$ &           37\,607\,912\,018 &        11 & \\
-	    13 &        9\,316\,358\,251\,200 &  10\,752 &     $-29$ &     $+37$ &          346\,065\,536\,839 &        12 & \\
-	    14 &       97\,821\,761\,637\,600 &  17\,280 &     $-27$ &     $+31$ &       3\,204\,941\,750\,802 &        12 & \\
-	    15 &      866\,421\,317\,361\,600 &  26\,880 &     $-11$ &     $+37$ &      29\,844\,570\,422\,669 &        13 & \\
-	    16 &   8\,086\,598\,962\,041\,600 &  41\,472 &     $-63$ &     $+61$ &     279\,238\,341\,033\,925 &        13 & \\
-	    17 &  74\,801\,040\,398\,884\,800 &  64\,512 &      $-3$ &      $+3$ &  2\,623\,557\,157\,654\,233 &        14 & \\
-	    18 & 897\,612\,484\,786\,617\,600 & 103\,680 &     $-11$ &      $+3$ & 24\,739\,954\,287\,740\,860 &        16 & \\
+	     1 &                            6 &        4 &      $-3$ &      $+1$ &                           4 &         2 \\
+	     2 &                           60 &       12 &      $-3$ &      $+1$ &                          25 &         3 \\
+	     3 &                          840 &       32 &      $-3$ &      $+9$ &                         168 &         4 \\
+	     4 &                       7\,560 &       64 &     $-27$ &      $+7$ &                      1\,229 &         5 \\
+	     5 &                      83\,160 &      128 &      $-9$ &      $+3$ &                      9\,592 &         6 \\
+	     6 &                     720\,720 &      240 &     $-17$ &      $+3$ &                     78\,498 &         7 \\
+	     7 &                  8\,648\,640 &      448 &      $-9$ &     $+19$ &                    664\,579 &         8 \\
+	     8 &                 73\,513\,440 &      768 &     $-11$ &      $+7$ &                 5\,761\,455 &         8 \\
+	     9 &                735\,134\,400 &   1\,344 &     $-63$ &      $+7$ &                50\,847\,534 &         9 \\
+	    10 &             6\,983\,776\,800 &   2\,304 &     $-33$ &     $+19$ &               455\,052\,511 &        10 \\
+	    11 &            97\,772\,875\,200 &   4\,032 &     $-23$ &      $+3$ &            4\,118\,054\,813 &        10 \\
+	    12 &           963\,761\,198\,400 &   6\,720 &     $-11$ &     $+39$ &           37\,607\,912\,018 &        11 \\
+	    13 &        9\,316\,358\,251\,200 &  10\,752 &     $-29$ &     $+37$ &          346\,065\,536\,839 &        12 \\
+	    14 &       97\,821\,761\,637\,600 &  17\,280 &     $-27$ &     $+31$ &       3\,204\,941\,750\,802 &        12 \\
+	    15 &      866\,421\,317\,361\,600 &  26\,880 &     $-11$ &     $+37$ &      29\,844\,570\,422\,669 &        13 \\
+	    16 &   8\,086\,598\,962\,041\,600 &  41\,472 &     $-63$ &     $+61$ &     279\,238\,341\,033\,925 &        13 \\
+	    17 &  74\,801\,040\,398\,884\,800 &  64\,512 &      $-3$ &      $+3$ &  2\,623\,557\,157\,654\,233 &        14 \\
+	    18 & 897\,612\,484\,786\,617\,600 & 103\,680 &     $-11$ &      $+3$ & 24\,739\,954\,287\,740\,860 &        16 \\
 	\hline
 \end{tabularx}
+\end{expandtable}
diff --git a/content/math/tables/probability.tex b/content/math/tables/probability.tex
index f265d10..29f92e1 100644
--- a/content/math/tables/probability.tex
+++ b/content/math/tables/probability.tex
@@ -1,19 +1,15 @@
-\begin{tabularx}{\linewidth}{|LICIR|}
+\begin{expandtable}
+\begin{tabularx}{\linewidth}{|LIR|}
 	\hline
-	\multicolumn{3}{|c|}{
+	\multicolumn{2}{|c|}{
 		Wahrscheinlichkeitstheorie ($A,B$ Ereignisse und $X,Y$ Variablen)
 	} \\
 	\hline
-	$\E(X + Y) = \E(X) + \E(Y)$ &
-	$\E(\alpha X) = \alpha \E(X)$ &
-	$X, Y$ unabh. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$\\
-	
-	$\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ &
-	$A, B$ disj. $\Leftrightarrow \Pr[A \land B] = \Pr[A] \cdot \Pr[B]$ &
-	$\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\
+	$\E(X + Y) = \E(X) + \E(Y)$                                & $\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ \\
+	$\E(\alpha X) = \alpha \E(X)$                              & $\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\
+	$X, Y$ unabh. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$ & $A, B$ disj. $\Leftrightarrow \Pr[A \land B] = \Pr[A] \cdot \Pr[B]$\\
 	\hline
 \end{tabularx}
-\vfill
 \begin{tabularx}{\linewidth}{|Xlr|lrX|}
 	\hline
 	\multicolumn{6}{|c|}{\textsc{Bertrand}'s Ballot Theorem (Kandidaten $A$ und $B$, $k \in \mathbb{N}$)} \\
@@ -25,3 +21,4 @@
 	$\#A \geq \#B + k$ & $Num = \frac{a - k + 1 - b}{a - k + 1} \binom{a + b - k}{b}$ & \\
 	\hline
 \end{tabularx}
+\end{expandtable}
diff --git a/content/math/tables/series.tex b/content/math/tables/series.tex
index 3042781..9618c2b 100644
--- a/content/math/tables/series.tex
+++ b/content/math/tables/series.tex
@@ -1,33 +1,33 @@
-\begin{tabularx}{\linewidth}{|XIXIXIX|}
-	\hline
-	\multicolumn{4}{|c|}{Reihen} \\
+\begin{expandtable}
+\begin{tabularx}{\linewidth}{|XIXIX|}
 	\hline
 	$\sum\limits_{i = 1}^n i = \frac{n(n+1)}{2}$ &
 	$\sum\limits_{i = 1}^n i^2 = \frac{n(n + 1)(2n + 1)}{6}$ &
-	$\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ &
-	$H_n = \sum\limits_{i = 1}^n \frac{1}{i}$ \\
+	$\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ \\
 	\grayhline
 	
-	$\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \quad c \neq 1$ &	
-	$\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \quad \vert c \vert < 1$ &
-	$\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \quad \vert c \vert < 1$ &	
-	$\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \quad \vert c \vert < 1$ \\
+	$\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \hfill c \neq 1$ &	
+	$\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \hfill \vert c \vert < 1$ &
+	$\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \hfill \vert c \vert < 1$ \\
 	\grayhline
-	
+		
 	\multicolumn{2}{|lI}{
 		$\sum\limits_{i = 0}^n ic^i = \frac{nc^{n + 2} - (n + 1)c^{n + 1} + c}{(c - 1)^2} \quad c \neq 1$
 	} &	
-	\multicolumn{2}{l|}{
+	$\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \hfill \vert c \vert < 1$ \\
+	\grayhline	
+	
+	\multicolumn{2}{|lI}{
 		$\sum\limits_{i = 1}^n iH_i = \frac{n(n + 1)}{2}H_n - \frac{n(n - 1)}{4}$
-	} \\
+	} &
+	$H_n = \sum\limits_{i = 1}^n \frac{1}{i}$ \\
 	\grayhline
 	
 	\multicolumn{2}{|lI}{
-		$\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$
-	} &
-	\multicolumn{2}{l|}{
 		$\sum\limits_{i = 1}^n \binom{i}{m}H_i =
 		\binom{n + 1}{m + 1} \left(H_{n + 1} - \frac{1}{m  + 1}\right)$
-	} \\
+	} &
+	$\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$ \\
 	\hline
 \end{tabularx}
+\end{expandtable}
diff --git a/content/math/tables/stuff.tex b/content/math/tables/stuff.tex
index 3cf8b4c..82f2d3f 100644
--- a/content/math/tables/stuff.tex
+++ b/content/math/tables/stuff.tex
@@ -1,6 +1,7 @@
-\begin{tabularx}{\linewidth}{|ll|}
+\begin{expandtable}
+\begin{tabularx}{\linewidth}{|Ll|}
 	\hline
-	\multicolumn{2}{|C|}{Verschiedenes} \\
+	\multicolumn{2}{|c|}{Verschiedenes} \\
 	\hline
 	Türme von Hanoi, minimale Schirttzahl: &
 	$T_n = 2^n - 1$ \\
@@ -20,7 +21,7 @@
 	\#Wälder mit $k$ gewurzelten Bäumen	&
 	$\frac{k}{n}\binom{n}{k}n^{n-k}$ \\
 
-	\#Wälder mit $k$ gewurzelten Bäumen mit vorgegebenen Wurzelknoten&
+	\#Wälder mit $k$ gewurzelten~Bäumen mit vorgegebenen Wurzelknoten&
 	$\frac{k}{n}n^{n-k}$ \\
 
 	Derangements &
@@ -29,4 +30,4 @@
 	$\lim\limits_{n \to \infty} \frac{!n}{n!} = \frac{1}{e}$ \\
 	\hline
 \end{tabularx}
-
+\end{expandtable}
diff --git a/content/math/transforms/seriesOperations.cpp b/content/math/transforms/seriesOperations.cpp
index 4743674..b405698 100644
--- a/content/math/transforms/seriesOperations.cpp
+++ b/content/math/transforms/seriesOperations.cpp
@@ -4,7 +4,7 @@ vector<ll> poly_inv(const vector<ll>& a, int n) {
 		vector<ll> a2 = a, q2 = q;
 		a2.resize(2*len), q2.resize(2*len);
 		ntt(q2);
-		for (int j : {0, 1}) {
+		for (int _ : {0, 1}) {
 			ntt(a2);
 			for (int i = 0; i < 2*len; i++) a2[i] = a2[i]*q2[i] % mod;
 			ntt(a2, true);
@@ -24,10 +24,13 @@ vector<ll> poly_deriv(vector<ll> a) {
 }
 
 vector<ll> poly_integr(vector<ll> a) {
-	if (a.empty()) return {0};
-	a.push_back(a.back() * powMod(sz(a), mod-2, mod) % mod);
-	for (int i = sz(a)-2; i > 0; i--)
-		a[i] = a[i-1] * powMod(i, mod-2, mod) % mod;
+	static vector<ll> inv = {0, 1};
+	for (static int i = 2; i <= sz(a); i++)
+		inv.push_back(mod - mod / i * inv[mod % i] % mod);
+
+	a.push_back(0);
+	for (int i = sz(a) - 1; i > 0; i--)
+		a[i] = a[i-1] * inv[i] % mod;
 	a[0] = 0;
 	return a;
 }
@@ -35,8 +38,7 @@ vector<ll> poly_integr(vector<ll> a) {
 vector<ll> poly_log(vector<ll> a, int n) {
 	a = mul(poly_deriv(a), poly_inv(a, n));
 	a.resize(n-1);
-	a = poly_integr(a);
-	return a;
+	return poly_integr(a);
 }
 
 vector<ll> poly_exp(vector<ll> a, int n) {