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// base and base_digits must be consistent
constexpr ll base = 1000000;
constexpr ll base_digits = 6;
struct bigint {
vll a; ll sign;
bigint() : sign(1) {}
bigint(ll v) {*this = v;}
bigint(const string &s) {read(s);}
void operator=(const bigint& v) {
sign = v.sign;
a = v.a;
}
void operator=(ll v) {
sign = 1;
if (v < 0) sign = -1, v = -v;
a.clear();
for (; v > 0; v = v / base)
a.push_back(v % base);
}
bigint operator+(const bigint& v) const {
if (sign == v.sign) {
bigint res = v;
for (ll i = 0, carry = 0; i < max(sz(a), sz(v.a)) || carry; ++i) {
if (i == sz(res.a))
res.a.push_back(0);
res.a[i] += carry + (i < sz(a) ? a[i] : 0);
carry = res.a[i] >= base;
if (carry)
res.a[i] -= base;
}
return res;
}
return *this - (-v);
}
bigint operator-(const bigint& v) const {
if (sign == v.sign) {
if (abs() >= v.abs()) {
bigint res = *this;
for (ll i = 0, carry = 0; i < sz(v.a) || carry; ++i) {
res.a[i] -= carry + (i < sz(v.a) ? v.a[i] : 0);
carry = res.a[i] < 0;
if (carry) res.a[i] += base;
}
res.trim();
return res;
}
return -(v - *this);
}
return *this + (-v);
}
void operator*=(ll v) {
if (v < 0) sign = -sign, v = -v;
for (ll i = 0, carry = 0; i < sz(a) || carry; ++i) {
if (i == sz(a)) a.push_back(0);
ll cur = a[i] * v + carry;
carry = cur / base;
a[i] = cur % base;
}
trim();
}
bigint operator*(ll v) const {
bigint res = *this;
res *= v;
return res;
}
friend pair<bigint, bigint> divmod(const bigint& a1, const bigint& b1) {
ll norm = base / (b1.a.back() + 1);
bigint a = a1.abs() * norm;
bigint b = b1.abs() * norm;
bigint q, r;
q.a.resize(sz(a.a));
for (ll i = sz(a.a) - 1; i >= 0; i--) {
r *= base;
r += a.a[i];
ll s1 = sz(r.a) <= sz(b.a) ? 0 : r.a[sz(b.a)];
ll s2 = sz(r.a) <= sz(b.a) - 1 ? 0 : r.a[sz(b.a) - 1];
ll d = (base * s1 + s2) / b.a.back();
r -= b * d;
while (r < 0) r += b, --d;
q.a[i] = d;
}
q.sign = a1.sign * b1.sign;
r.sign = a1.sign;
q.trim();
r.trim();
return make_pair(q, r / norm);
}
bigint operator/(const bigint& v) const {
return divmod(*this, v).first;
}
bigint operator%(const bigint& v) const {
return divmod(*this, v).second;
}
void operator/=(ll v) {
if (v < 0) sign = -sign, v = -v;
for (ll i = sz(a) - 1, rem = 0; i >= 0; --i) {
ll cur = a[i] + rem * base;
a[i] = cur / v;
rem = cur % v;
}
trim();
}
bigint operator/(ll v) const {
bigint res = *this;
res /= v;
return res;
}
ll operator%(ll v) const {
if (v < 0) v = -v;
ll m = 0;
for (ll i = sz(a) - 1; i >= 0; --i)
m = (a[i] + m * base) % v;
return m * sign;
}
void operator+=(const bigint& v) {
*this = *this + v;
}
void operator-=(const bigint& v) {
*this = *this - v;
}
void operator*=(const bigint& v) {
*this = *this * v;
}
void operator/=(const bigint& v) {
*this = *this / v;
}
bool operator<(const bigint& v) const {
if (sign != v.sign) return sign < v.sign;
if (sz(a) != sz(v.a))
return sz(a) * sign < sz(v.a) * v.sign;
for (ll i = sz(a) - 1; i >= 0; i--)
if (a[i] != v.a[i])
return a[i] * sign < v.a[i] * sign;
return false;
}
bool operator>(const bigint& v) const {
return v < *this;
}
bool operator<=(const bigint& v) const {
return !(v < *this);
}
bool operator>=(const bigint& v) const {
return !(*this < v);
}
bool operator==(const bigint& v) const {
return !(*this < v) && !(v < *this);
}
bool operator!=(const bigint& v) const {
return *this < v || v < *this;
}
void trim() {
while (!a.empty() && !a.back()) a.pop_back();
if (a.empty()) sign = 1;
}
bool isZero() const {
return a.empty() || (sz(a) == 1 && a[0] == 0);
}
bigint operator-() const {
bigint res = *this;
res.sign = -sign;
return res;
}
bigint abs() const {
bigint res = *this;
res.sign *= res.sign;
return res;
}
ll longValue() const {
ll res = 0;
for (ll i = sz(a) - 1; i >= 0; i--)
res = res * base + a[i];
return res * sign;
}
void read(const string& s) {
sign = 1;
a.clear();
ll pos = 0;
while (pos < sz(s) && (s[pos] == '-' || s[pos] == '+')) {
if (s[pos] == '-') sign = -sign;
++pos;
}
for (ll i = sz(s) - 1; i >= pos; i -= base_digits) {
ll x = 0;
for (ll j = max(pos, i - base_digits + 1); j <= i; j++)
x = x * 10 + s[j] - '0';
a.push_back(x);
}
trim();
}
friend istream& operator>>(istream& stream, bigint& v) {
string s;
stream >> s;
v.read(s);
return stream;
}
friend ostream& operator<<(ostream& stream, const bigint& v) {
if (v.sign == -1) stream << '-';
stream << (v.a.empty() ? 0 : v.a.back());
for (ll i = sz(v.a) - 2; i >= 0; --i)
stream << setw(base_digits) << setfill('0') << v.a[i];
return stream;
}
static vll karatsubaMultiply(const vll& a, const vll& b) {
ll n = sz(a);
vll res(n + n);
if (n <= 32) {
for (ll i = 0; i < n; i++)
for (ll j = 0; j < n; j++)
res[i + j] += a[i] * b[j];
return res;
}
ll k = n >> 1;
vll a1(a.begin(), a.begin() + k);
vll a2(a.begin() + k, a.end());
vll b1(b.begin(), b.begin() + k);
vll b2(b.begin() + k, b.end());
vll a1b1 = karatsubaMultiply(a1, b1);
vll a2b2 = karatsubaMultiply(a2, b2);
for (ll i = 0; i < k; i++) a2[i] += a1[i];
for (ll i = 0; i < k; i++) b2[i] += b1[i];
vll r = karatsubaMultiply(a2, b2);
for (ll i = 0; i < sz(a1b1); i++) r[i] -= a1b1[i];
for (ll i = 0; i < sz(a2b2); i++) r[i] -= a2b2[i];
for (ll i = 0; i < sz(r); i++) res[i + k] += r[i];
for (ll i = 0; i < sz(a1b1); i++) res[i] += a1b1[i];
for (ll i = 0; i < sz(a2b2); i++) res[i + n] += a2b2[i];
return res;
}
bigint operator*(const bigint& v) const {
vll a(this->a.begin(), this->a.end());
vll b(v.a.begin(), v.a.end());
while (sz(a) < sz(b)) a.push_back(0);
while (sz(b) < sz(a)) b.push_back(0);
while (sz(a) & (sz(a) - 1))
a.push_back(0), b.push_back(0);
vll c = karatsubaMultiply(a, b);
bigint res;
res.sign = sign * v.sign;
for (ll i = 0, carry = 0; i < sz(c); i++) {
ll cur = c[i] + carry;
res.a.push_back(cur % base);
carry = cur / base;
}
res.trim();
return res;
}
};
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