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#include "math/ntt.hpp"
<typename mint> ntt(vector<mint> &a) $a$ 自身を NTT した結果に更新する。列長 $n$ は 2 冪である必要がある。 $O(n\log n)$ 時間。
<typename mint> ntt(vector<mint> &a)
<typename mint> intt(vector<mint> &a) $a$ 自身を逆 NTT した結果に更新する。列長 $n$ は 2 冪である必要がある。 $O(n\log n)$ 時間。
<typename mint> intt(vector<mint> &a)
#pragma once #include "../template.hpp" template <typename mint> void ntt(vector<mint> &a, bool inv = false) { ll n = a.size(), m = n >> 1; mint root = 2; while (root.pow((mint::mod() - 1) >> 1) == 1) root += 1; mint wn = root.pow((mint::mod() - 1) / n); if (inv) wn = wn.inv(); vector<mint> b(n); for (ll i = 1; i < n; i <<= 1, wn *= wn, swap(a, b)) { mint wj = 1; for (ll j = 0; j < m; j += i, wj *= wn) { for (ll k : rep(i)) { b[0 + (j << 1) + k] = (a[0 + j + k] + a[m + j + k]); b[i + (j << 1) + k] = (a[0 + j + k] - a[m + j + k]) * wj; } } } if (inv) { mint ninv = mint(n).inv(); for (mint &ai : a) ai *= ninv; } } template <typename mint> void intt(vector<mint> &a) { ntt(a, true); }
#line 2 "math/ntt.hpp" #line 2 "template.hpp" #include <bits/stdc++.h> using namespace std; #define all(a) begin(a), end(a) #define rall(a) rbegin(a), rend(a) #define uniq(a) (a).erase(unique(all(a)), (a).end()) #define t0 first #define t1 second using ll = long long; using ull = unsigned long long; using pll = pair<ll, ll>; using vll = vector<ll>; constexpr double pi = 3.14159265358979323846; constexpr ll dy[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0}; constexpr ll dx[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0}; constexpr ll sign(ll a) { return (a > 0) - (a < 0); } constexpr ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } constexpr ll cdiv(ll a, ll b) { return -fdiv(-a, b); } constexpr ll pw(ll n) { return 1ll << n; } constexpr ll flg(ll n) { return 63 - __builtin_clzll(n); } constexpr ll clg(ll n) { return n == 1 ? 0 : flg(n - 1) + 1; } constexpr ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; } template <typename T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>; template <typename T> constexpr T sq(const T &a) { return a * a; } template <typename T, typename U> constexpr bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; } template <typename T, typename U> constexpr bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; } template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &a) { os << "(" << a.first << ", " << a.second << ")"; return os; } template <typename T, typename U, typename V> ostream &operator<<(ostream &os, const tuple<T, U, V> &a) { os << "(" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a) << ")"; return os; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } template <typename T> ostream &operator<<(ostream &os, const set<T> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } template <typename T> ostream &operator<<(ostream &os, const multiset<T> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } #ifdef ONLINE_JUDGE #define dump(...) (void(0)) #else void debug() { cerr << endl; } template <typename Head, typename... Tail> void debug(Head &&head, Tail &&... tail) { cerr << head; if (sizeof...(Tail)) cerr << ", "; debug(tail...); } #define dump(...) cerr << __LINE__ << ": " << #__VA_ARGS__ << " = ", debug(__VA_ARGS__) #endif struct rep { struct itr { ll v; itr(ll v) : v(v) {} void operator++() { ++v; } ll operator*() const { return v; } bool operator!=(itr i) const { return v < *i; } }; ll l, r; rep(ll l, ll r) : l(l), r(r) {} rep(ll r) : rep(0, r) {} itr begin() const { return l; }; itr end() const { return r; }; }; struct per { struct itr { ll v; itr(ll v) : v(v) {} void operator++() { --v; } ll operator*() const { return v; } bool operator!=(itr i) const { return v > *i; } }; ll l, r; per(ll l, ll r) : l(l), r(r) {} per(ll r) : per(0, r) {} itr begin() const { return r - 1; }; itr end() const { return l - 1; }; }; struct io_setup { static constexpr int PREC = 20; io_setup() { cout << fixed << setprecision(PREC); cerr << fixed << setprecision(PREC); }; } iOS; #line 4 "math/ntt.hpp" template <typename mint> void ntt(vector<mint> &a, bool inv = false) { ll n = a.size(), m = n >> 1; mint root = 2; while (root.pow((mint::mod() - 1) >> 1) == 1) root += 1; mint wn = root.pow((mint::mod() - 1) / n); if (inv) wn = wn.inv(); vector<mint> b(n); for (ll i = 1; i < n; i <<= 1, wn *= wn, swap(a, b)) { mint wj = 1; for (ll j = 0; j < m; j += i, wj *= wn) { for (ll k : rep(i)) { b[0 + (j << 1) + k] = (a[0 + j + k] + a[m + j + k]); b[i + (j << 1) + k] = (a[0 + j + k] - a[m + j + k]) * wj; } } } if (inv) { mint ninv = mint(n).inv(); for (mint &ai : a) ai *= ninv; } } template <typename mint> void intt(vector<mint> &a) { ntt(a, true); }