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#include "../../util.h"
#include <math/modPowIterativ.cpp>
#include <math/transforms/ntt.cpp>
#include <math/transforms/multiplyNTT.cpp>
#pragma GCC diagnostic ignored "-Wunused-variable"
#include <math/transforms/seriesOperations.cpp>
namespace reference {//checked against yosupo
vector<ll> poly_inv(vector<ll> a, int n){
vector<ll> q = {powMod(a[0], mod-2, mod)};
for(int len = 1; len < n; len *= 2){
vector<ll> a2 = a, q2 = q;
a2.resize(2*len), q2.resize(2*len);
ntt(q2);
for(int j = 0; j < 2; j++){
ntt(a2);
for(int i = 0; i < 2*len; i++) a2[i] = a2[i] * q2[i] % mod;
ntt(a2, true);
for(int i = 0; i < len; i++) a2[i] = 0;
}
for(int i = len; i < min(n, 2*len); i++) q.push_back((mod - a2[i]) % mod);
}
return q;
}
vector<ll> poly_deriv(vector<ll> a){
for(int i = 0; i < ssize(a)-1; i++)
a[i] = a[i+1] * (i+1) % mod;
a.pop_back();
return a;
}
vector<ll> poly_integr(vector<ll> a){
if(a.empty()) return {0};
a.push_back(a.back() * powMod(ssize(a), mod-2, mod) % mod);
for(int i = ssize(a)-2; i > 0; i--)
a[i] = a[i-1] * powMod(i, mod-2, mod) % mod;
a[0] = 0;
return 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;
}
vector<ll> poly_exp(vector<ll> a, int n){
vector<ll> q = {1};
for(int len = 1; len < n; len *= 2){
vector<ll> p = poly_log(q, 2*len);
for(int i = 0; i < 2*len; i++)
p[i] = (mod - p[i] + (i < ssize(a) ? a[i] : 0)) % mod;
vector<ll> q2 = q;
q2.resize(2*len);
ntt(p), ntt(q2);
for(int i = 0; i < 2*len; i++) p[i] = p[i] * q2[i] % mod;
ntt(p, true);
for(int i = len; i < min(n, 2*len); i++) q.push_back(p[i]);
}
return q;
}
}
void test_inv() {
ll queries = 0;
for (ll i = 0; i < 50'000; i++) {
int n = Random::integer<int>(1, 100);
int m = Random::integer<int>(1, 100);
vector<ll> a = Random::integers<ll>(n, 0, mod);
auto got = poly_inv(a, m);
auto expected = reference::poly_inv(a, m);
if (got != expected) cerr << "error" << FAIL;
queries += n;
}
cerr << "tested inv: " << queries << endl;
}
void test_deriv() {
ll queries = 0;
for (ll i = 0; i < 50'000; i++) {
int n = Random::integer<int>(1, 100);
vector<ll> a = Random::integers<ll>(n, 0, mod);
auto got = poly_deriv(a);
auto expected = reference::poly_deriv(a);
if (got != expected) cerr << "error" << FAIL;
queries += n;
}
cerr << "tested deriv: " << queries << endl;
}
void test_integr() {
ll queries = 0;
for (ll i = 0; i < 50'000; i++) {
int n = Random::integer<int>(1, 100);
vector<ll> a = Random::integers<ll>(n, 0, mod);
auto got = poly_deriv(a);
auto expected = reference::poly_deriv(a);
if (got != expected) cerr << "error" << FAIL;
queries += n;
}
cerr << "tested integr: " << queries << endl;
}
void test_log() {
ll queries = 0;
for (ll i = 0; i < 50'000; i++) {
int n = Random::integer<int>(1, 100);
int m = Random::integer<int>(1, 100);
vector<ll> a = Random::integers<ll>(n, 0, mod);
auto got = poly_log(a, m);
auto expected = reference::poly_log(a, m);
if (got != expected) cerr << "error" << FAIL;
queries += n;
}
cerr << "tested log: " << queries << endl;
}
void test_exp() {
ll queries = 0;
for (ll i = 0; i < 50'000; i++) {
int n = Random::integer<int>(1, 100);
int m = Random::integer<int>(1, 100);
vector<ll> a = Random::integers<ll>(n, 0, mod);
auto got = poly_exp(a, m);
auto expected = reference::poly_exp(a, m);
if (got != expected) cerr << "error" << FAIL;
queries += n;
}
cerr << "tested exp: " << queries << endl;
}
int main() {
test_inv();
test_deriv();
test_integr();
test_log();
test_exp();
}
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