結果

問題 No.2936 Sum of Square of Mex
ユーザー ecotteaecottea
提出日時 2024-10-13 01:25:08
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
実行時間 -
コード長 27,306 bytes
コンパイル時間 8,339 ms
コンパイル使用メモリ 353,888 KB
実行使用メモリ 122,660 KB
最終ジャッジ日時 2024-10-13 01:25:21
合計ジャッジ時間 12,366 ms
ジャッジサーバーID
(参考情報)
judge3 / judge5
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
13,632 KB
testcase_01 AC 1 ms
6,816 KB
testcase_02 AC 507 ms
24,208 KB
testcase_03 AC 3 ms
6,816 KB
testcase_04 AC 2 ms
6,816 KB
testcase_05 AC 2 ms
6,816 KB
testcase_06 AC 2 ms
6,816 KB
testcase_07 AC 2 ms
6,816 KB
testcase_08 TLE -
testcase_09 -- -
testcase_10 -- -
testcase_11 -- -
testcase_12 -- -
testcase_13 -- -
testcase_14 -- -
testcase_15 -- -
testcase_16 -- -
testcase_17 -- -
testcase_18 -- -
testcase_19 -- -
testcase_20 -- -
testcase_21 -- -
testcase_22 -- -
testcase_23 -- -
testcase_24 -- -
testcase_25 -- -
testcase_26 -- -
testcase_27 -- -
testcase_28 -- -
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ソースコード

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// QCFium
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; using ull = unsigned long long; // -2^63 2^63 = 9e18int -2^31 2^31 = 2e9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) //
//
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // mod
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
using mint = modint998244353;
//using mint = static_modint<1000000007>;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
template <size_t N> inline int lsb(const bitset<N>& b) { return b._Find_first(); }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(...)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE MLE
#endif
//
/*
* MFPS() : O(1)
* f = 0
*
* MFPS(mint c0) : O(1)
* f = c0
*
* MFPS(mint c0, int n) : O(n)
* n f = c0
*
* MFPS(vm c) : O(n)
* f(z) = c[0] + c[1] z + ... + c[n - 1] z^(n-1)
*
* set_conv(vm(*CONV)(const vm&, const vm&)) : O(1)
* CONV
*
* c + f, f + c : O(1) f + g : O(n)
* f - c : O(1) c - f, f - g, -f : O(n)
* c * f, f * c : O(n) f * g : O(n log n) f * g_sp : O(n |g|)
* f / c : O(n) f / g : O(n log n) f / g_sp : O(n |g|)
*
* g_sp {, } vector
* : g(0) != 0
*
* MFPS f.inv(int d) : O(n log n)
* 1 / f mod z^d
* : f(0) != 0
*
* MFPS f.quotient(MFPS g) : O(n log n)
* MFPS f.reminder(MFPS g) : O(n log n)
* pair<MFPS, MFPS> f.quotient_remainder(MFPS g) : O(n log n)
* f g
* : g 0
*
* int f.deg(), int f.size() : O(1)
* f []
*
* MFPS::monomial(int d, mint c = 1) : O(d)
* c z^d
*
* mint f.assign(mint c) : O(n)
* f z c
*
* f.resize(int d) : O(1)
* mod z^d
*
* f.resize() : O(n)
*
*
* f >> d, f << d : O(n)
* d []
* z^d z^d
*
* f.push_back(c) : O(1)
* c
*/
struct MFPS {
using SMFPS = vector<pim>;
int n; // + 1
vm c; //
inline static vm(*CONV)(const vm&, const vm&) = convolution; //
// 0
MFPS() : n(0) {}
MFPS(mint c0) : n(1), c({ c0 }) {}
MFPS(int c0) : n(1), c({ mint(c0) }) {}
MFPS(mint c0, int d) : n(d), c(n) { c[0] = c0; }
MFPS(int c0, int d) : n(d), c(n) { c[0] = c0; }
MFPS(const vm& c_) : n(sz(c_)), c(c_) {}
MFPS(const vi& c_) : n(sz(c_)), c(n) { rep(i, n) c[i] = c_[i]; }
//
MFPS(const MFPS& f) = default;
MFPS& operator=(const MFPS& f) = default;
MFPS& operator=(const mint& c0) { n = 1; c = { c0 }; return *this; }
void push_back(mint cn) { c.emplace_back(cn); ++n; }
void pop_back() { c.pop_back(); --n; }
[[nodiscard]] mint back() { return c.back(); }
//
[[nodiscard]] bool operator==(const MFPS& g) const { return c == g.c; }
[[nodiscard]] bool operator!=(const MFPS& g) const { return c != g.c; }
//
inline mint const& operator[](int i) const { return c[i]; }
inline mint& operator[](int i) { return c[i]; }
//
[[nodiscard]] int deg() const { return n - 1; }
[[nodiscard]] int size() const { return n; }
static void set_conv(vm(*CONV_)(const vm&, const vm&)) {
// verify : https://atcoder.jp/contests/tdpc/tasks/tdpc_fibonacci
CONV = CONV_;
}
//
MFPS& operator+=(const MFPS& g) {
if (n >= g.n) rep(i, g.n) c[i] += g.c[i];
else {
rep(i, n) c[i] += g.c[i];
repi(i, n, g.n - 1) c.push_back(g.c[i]);
n = g.n;
}
return *this;
}
[[nodiscard]] MFPS operator+(const MFPS& g) const { return MFPS(*this) += g; }
//
MFPS& operator+=(const mint& sc) {
if (n == 0) { n = 1; c = { sc }; }
else { c[0] += sc; }
return *this;
}
[[nodiscard]] MFPS operator+(const mint& sc) const { return MFPS(*this) += sc; }
[[nodiscard]] friend MFPS operator+(const mint& sc, const MFPS& f) { return f + sc; }
MFPS& operator+=(const int& sc) { *this += mint(sc); return *this; }
[[nodiscard]] MFPS operator+(const int& sc) const { return MFPS(*this) += sc; }
[[nodiscard]] friend MFPS operator+(const int& sc, const MFPS& f) { return f + sc; }
//
MFPS& operator-=(const MFPS& g) {
if (n >= g.n) rep(i, g.n) c[i] -= g.c[i];
else {
rep(i, n) c[i] -= g.c[i];
repi(i, n, g.n - 1) c.push_back(-g.c[i]);
n = g.n;
}
return *this;
}
[[nodiscard]] MFPS operator-(const MFPS& g) const { return MFPS(*this) -= g; }
//
MFPS& operator-=(const mint& sc) { *this += -sc; return *this; }
[[nodiscard]] MFPS operator-(const mint& sc) const { return MFPS(*this) -= sc; }
[[nodiscard]] friend MFPS operator-(const mint& sc, const MFPS& f) { return -(f - sc); }
MFPS& operator-=(const int& sc) { *this += -sc; return *this; }
[[nodiscard]] MFPS operator-(const int& sc) const { return MFPS(*this) -= sc; }
[[nodiscard]] friend MFPS operator-(const int& sc, const MFPS& f) { return -(f - sc); }
//
[[nodiscard]] MFPS operator-() const { return MFPS(*this) *= -1; }
//
MFPS& operator*=(const mint& sc) { rep(i, n) c[i] *= sc; return *this; }
[[nodiscard]] MFPS operator*(const mint& sc) const { return MFPS(*this) *= sc; }
[[nodiscard]] friend MFPS operator*(const mint& sc, const MFPS& f) { return f * sc; }
MFPS& operator*=(const int& sc) { *this *= mint(sc); return *this; }
[[nodiscard]] MFPS operator*(const int& sc) const { return MFPS(*this) *= sc; }
[[nodiscard]] friend MFPS operator*(const int& sc, const MFPS& f) { return f * sc; }
//
MFPS& operator/=(const mint& sc) { *this *= sc.inv(); return *this; }
[[nodiscard]] MFPS operator/(const mint& sc) const { return MFPS(*this) /= sc; }
MFPS& operator/=(const int& sc) { *this /= mint(sc); return *this; }
[[nodiscard]] MFPS operator/(const int& sc) const { return MFPS(*this) /= sc; }
//
MFPS& operator*=(const MFPS& g) { c = CONV(c, g.c); n = sz(c); return *this; }
[[nodiscard]] MFPS operator*(const MFPS& g) const { return MFPS(*this) *= g; }
//
[[nodiscard]] MFPS inv(int d) const {
// https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
// verify : https://judge.yosupo.jp/problem/inv_of_formal_power_series
//
// 1 / f mod z^d
// f g = 1 (mod z^d)
// g
// d 1, 2, 4, ..., 2^i
//
// d = 1
// g = 1 / f[0] (mod z^1)
//
//
//
// g = h (mod z^k)
//
// g mod z^(2 k)
//
// g - h = 0 (mod z^k)
// ⇒ (g - h)^2 = 0 (mod z^(2 k))
// ⇔ g^2 - 2 g h + h^2 = 0 (mod z^(2 k))
// ⇒ f g^2 - 2 f g h + f h^2 = 0 (mod z^(2 k))
// ⇔ g - 2 h + f h^2 = 0 (mod z^(2 k))  (f g = 1 (mod z^d) )
// ⇔ g = (2 - f h) h (mod z^(2 k))
//
//
// d ≦ 2^i i d
Assert(!c.empty());
Assert(c[0] != 0);
MFPS g(c[0].inv());
for (int k = 1; k < d; k <<= 1) {
int len = max(min(2 * k, d), 1);
MFPS tmp(0, len);
rep(i, min(len, n)) tmp[i] = -c[i]; // -f
tmp *= g; // -f h
tmp.resize(len);
tmp[0] += 2; // 2 - f h
g *= tmp; // (2 - f h) h
g.resize(len);
}
return g;
}
MFPS& operator/=(const MFPS& g) { return *this *= g.inv(max(n, g.n)); }
[[nodiscard]] MFPS operator/(const MFPS& g) const { return MFPS(*this) /= g; }
//
[[nodiscard]] MFPS quotient(const MFPS& g) const {
// : https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
// verify : https://judge.yosupo.jp/problem/division_of_polynomials
//
// f(x) = g(x) q(x) + r(x) q(x)
// f n-1, g m-1 (n ≧ m)
// q n-mr m-2
//
// f^R f
// f^R(x) := f(1/x) x^(n-1)
//
//
// x → 1/x
// f(1/x) = g(1/x) q(1/x) + r(1/x)
// ⇔ f(1/x) x^(n-1) = g(1/x) q(1/x) x^(n-1) + r(1/x) x^(n-1)
// ⇔ f(1/x) x^(n-1) = g(1/x) x^(m-1) q(1/x) x^(n-m) + r(1/x) x^(m-2) x^(n-m+1)
// ⇔ f^R(x) = g^R(x) q^R(x) + r^R(x) x^(n-m+1)
// ⇒ f^R(x) = g^R(x) q^R(x) (mod x^(n-m+1))
// ⇒ q^R(x) = f^R(x) / g^R(x) (mod x^(n-m+1))
//
//
// q mod x^(n-m+1)
// q n-m q
if (n < g.n) return MFPS();
return ((this->rev() / g.rev()).resize(n - g.n + 1)).rev();
}
[[nodiscard]] MFPS reminder(const MFPS& g) const {
// verify : https://judge.yosupo.jp/problem/division_of_polynomials
return (*this - this->quotient(g) * g).resize();
}
[[nodiscard]] pair<MFPS, MFPS> quotient_remainder(const MFPS& g) const {
// verify : https://judge.yosupo.jp/problem/division_of_polynomials
pair<MFPS, MFPS> res;
res.first = this->quotient(g);
res.second = (*this - res.first * g).resize();
return res;
}
//
MFPS& operator*=(const SMFPS& g) {
// g
auto it0 = g.begin();
mint g0 = 0;
if (it0->first == 0) {
g0 = it0->second;
it0++;
}
// DP
repir(i, n - 1, 0) {
//
for (auto it = it0; it != g.end(); it++) {
auto [j, gj] = *it;
if (i + j >= n) break;
c[i + j] += c[i] * gj;
}
//
c[i] *= g0;
}
return *this;
}
[[nodiscard]] MFPS operator*(const SMFPS& g) const { return MFPS(*this) *= g; }
//
MFPS& operator/=(const SMFPS& g) {
// g
auto it0 = g.begin();
Assert(it0->first == 0 && it0->second != 0);
mint g0_inv = it0->second.inv();
it0++;
// DP
rep(i, n) {
//
c[i] *= g0_inv;
//
for (auto it = it0; it != g.end(); it++) {
auto [j, gj] = *it;
if (i + j >= n) break;
c[i + j] -= c[i] * gj;
}
}
return *this;
}
[[nodiscard]] MFPS operator/(const SMFPS& g) const { return MFPS(*this) /= g; }
//
[[nodiscard]] MFPS rev() const { MFPS h = *this; reverse(all(h.c)); return h; }
//
[[nodiscard]] static MFPS monomial(int d, mint coef = 1) {
MFPS mono(0, d + 1);
mono[d] = coef;
return mono;
}
//
MFPS& resize() {
// 0
while (n > 0 && c[n - 1] == 0) {
c.pop_back();
n--;
}
return *this;
}
// x^d
MFPS& resize(int d) {
n = d;
c.resize(d);
return *this;
}
//
[[nodiscard]] mint assign(const mint& x) const {
mint val = 0;
repir(i, n - 1, 0) val = val * x + c[i];
return val;
}
//
MFPS& operator>>=(int d) {
n += d;
c.insert(c.begin(), d, 0);
return *this;
}
MFPS& operator<<=(int d) {
n -= d;
if (n <= 0) { c.clear(); n = 0; }
else c.erase(c.begin(), c.begin() + d);
return *this;
}
[[nodiscard]] MFPS operator>>(int d) const { return MFPS(*this) >>= d; }
[[nodiscard]] MFPS operator<<(int d) const { return MFPS(*this) <<= d; }
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const MFPS& f) {
if (f.n == 0) os << 0;
else {
rep(i, f.n) {
os << f[i] << "z^" << i;
if (i < f.n - 1) os << " + ";
}
}
return os;
}
#endif
};
//
/*
* Factorial_mint(int N) : O(n)
* N
*
* mint fact(int n) : O(1)
* n!
*
* mint fact_inv(int n) : O(1)
* 1/n! n 0
*
* mint inv(int n) : O(1)
* 1/n
*
* mint perm(int n, int r) : O(1)
* nPr
*
* mint bin(int n, int r) : O(1)
* nCr
*
* mint bin_inv(int n, int r) : O(1)
* 1/nCr
*
* mint mul(vi rs) : O(|rs|)
* nC[rs] n = Σrs
*
* mint hom(int n, int r) : O(1)
* nHr = n+r-1Cr 0H0 = 1
*
* mint neg_bin(int n, int r) : O(1)
* nCr = (-1)^r -n+r-1Cr n ≦ 0, r ≧ 0
*/
class Factorial_mint {
int n_max;
//
vm fac, fac_inv;
public:
// n! O(n)
Factorial_mint(int n) : n_max(n), fac(n + 1), fac_inv(n + 1) {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
fac[0] = 1;
repi(i, 1, n) fac[i] = fac[i - 1] * i;
fac_inv[n] = fac[n].inv();
repir(i, n - 1, 0) fac_inv[i] = fac_inv[i + 1] * (i + 1);
}
Factorial_mint() : n_max(0) {} //
// n!
mint fact(int n) const {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
Assert(0 <= n && n <= n_max);
return fac[n];
}
// 1/n! n 0
mint fact_inv(int n) const {
// verify : https://atcoder.jp/contests/abc289/tasks/abc289_h
Assert(n <= n_max);
if (n < 0) return 0;
return fac_inv[n];
}
// 1/n
mint inv(int n) const {
// verify : https://atcoder.jp/contests/exawizards2019/tasks/exawizards2019_d
Assert(0 < n && n <= n_max);
return fac[n - 1] * fac_inv[n];
}
// nPr
mint perm(int n, int r) const {
// verify : https://atcoder.jp/contests/abc172/tasks/abc172_e
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[n - r];
}
// nCr
mint bin(int n, int r) const {
// verify : https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[r] * fac_inv[n - r];
}
// 1/nCr
mint bin_inv(int n, int r) const {
// verify : https://www.codechef.com/problems/RANDCOLORING
Assert(n <= n_max);
Assert(r >= 0 && n - r >= 0);
return fac_inv[n] * fac[r] * fac[n - r];
}
// nC[rs]
mint mul(const vi& rs) const {
// verify : https://yukicoder.me/problems/no/2141
if (*min_element(all(rs)) < 0) return 0;
int n = accumulate(all(rs), 0);
Assert(n <= n_max);
mint res = fac[n];
repe(r, rs) res *= fac_inv[r];
return res;
}
// nHr = n+r-1Cr 0H0 = 1
mint hom(int n, int r) {
// verify : https://mojacoder.app/users/riantkb/problems/toj_ex_2
if (n == 0) return (int)(r == 0);
Assert(n + r - 1 <= n_max);
if (r < 0 || n - 1 < 0) return 0;
return fac[n + r - 1] * fac_inv[r] * fac_inv[n - 1];
}
// nCr n ≦ 0, r ≧ 0
mint neg_bin(int n, int r) {
// verify : https://atcoder.jp/contests/abc345/tasks/abc345_g
if (n == 0) return (int)(r == 0);
Assert(-n + r - 1 <= n_max);
if (r < 0 || -n - 1 < 0) return 0;
return (r & 1 ? -1 : 1) * fac[-n + r - 1] * fac_inv[r] * fac_inv[-n - 1];
}
};
//mod 998244353O((ha + hb) (wa + wb) (log(ha + hb) + log(wa + wb)))
/*
* a[0..ha)[0..wa) b[0..hb)[0..wb)
*/
vvm convolution_2D(vvm a, vvm b) {
// verify : https://atcoder.jp/contests/abc345/tasks/abc345_g
int ha = sz(a), wa = sz(a[0]);
int hb = sz(b), wb = sz(b[0]);
//
if ((ll)ha * wa * hb * wb <= 100000LL) {
vvm c(ha + hb - 1, vm(wa + wb - 1));
rep(ia, ha) rep(ib, hb) rep(ja, wa) rep(jb, wb) {
c[ia + ib][ja + jb] += a[ia][ja] * b[ib][jb];
}
return c;
}
// NTT
if ((ll)ha * hb <= 800LL) {
// 2
int W = 1 << (msb(wa + wb - 2) + 1);
rep(i, ha) a[i].resize(W);
rep(i, hb) b[i].resize(W);
// NTT
rep(i, ha) internal::butterfly(a[i]);
rep(i, hb) internal::butterfly(b[i]);
vvm c(ha + hb - 1, vm(wa + wb - 1)); vm tmp(W);
rep(ia, ha) rep(ib, hb) {
//
rep(j, W) tmp[j] = a[ia][j] * b[ib][j];
// INTT
internal::butterfly_inv(tmp);
rep(j, wa + wb - 1) c[ia + ib][j] += tmp[j];
}
// 調
mint inv = mint(W).inv();
rep(i, ha + hb - 1) rep(j, wa + wb - 1) c[i][j] *= inv;
return c;
}
// NTT
if ((ll)wa * wb <= 800LL) {
// 2
int H = 1 << (msb(ha + hb - 2) + 1);
vvm aT(wa, vm(H)), bT(wb, vm(H));
rep(i, ha) rep(j, wa) aT[j][i] = a[i][j];
rep(i, hb) rep(j, wb) bT[j][i] = b[i][j];
// NTT
rep(j, wa) internal::butterfly(aT[j]);
rep(j, wb) internal::butterfly(bT[j]);
vvm c(ha + hb - 1, vm(wa + wb - 1)); vm tmp(H);
rep(ja, wa) rep(jb, wb) {
//
rep(i, H) tmp[i] = aT[ja][i] * bT[jb][i];
// INTT
internal::butterfly_inv(tmp);
rep(i, ha + hb - 1) c[i][ja + jb] += tmp[i];
}
// 調
mint inv = mint(H).inv();
rep(i, ha + hb - 1) rep(j, wa + wb - 1) c[i][j] *= inv;
return c;
}
// NTT
// 2
int H = 1 << (msb(ha + hb - 2) + 1);
int W = 1 << (msb(wa + wb - 2) + 1);
a.resize(H); b.resize(H);
rep(i, H) { a[i].resize(W); b[i].resize(W); }
// NTT
rep(i, H) { internal::butterfly(a[i]); internal::butterfly(b[i]); }
//
vvm aT(W, vm(H)), bT(W, vm(H));
rep(i, H) rep(j, W) { aT[j][i] = a[i][j]; bT[j][i] = b[i][j]; }
// NTT
rep(j, W) { internal::butterfly(aT[j]); internal::butterfly(bT[j]); }
//
rep(j, W) rep(i, H) aT[j][i] *= bT[j][i];
// INTT
rep(j, W) internal::butterfly_inv(aT[j]);
//
rep(i, H) rep(j, W) a[i][j] = aT[j][i];
// INTT
rep(i, H) internal::butterfly_inv(a[i]);
//
a.resize(ha + hb - 1);
rep(i, ha + hb - 1) a[i].resize(wa + wb - 1);
// 調
mint inv = mint(H * W).inv();
rep(i, ha + hb - 1) rep(j, wa + wb - 1) a[i][j] *= inv;
return a;
}
//O(n m^2 (log n + log m) log N) ?
/*
* f(z,w) = Σi∈[0..n) Σj∈[0..m) f[i][j] z^i w^j
* g(z,w) = Σi∈[0..n) Σj∈[0..m) g[i][j] z^i w^j
* [z^N] [w^[0..M]] f(z,w) / g(z,w)
*
* : [z^0]g(z,w) = 1
*
* mod 998244353
*/
vm bostan_mori(vvm f, vvm g, int N, int M) {
// : https://noshi91.hatenablog.com/entry/2024/03/16/224034
// verify : https://judge.yosupo.jp/problem/compositional_inverse_of_formal_power_series_large
//
// 1 -
// f(z,w) = 0 0
if (sz(f) == 0) return vm(M + 1);
while (N > 0) {
// f2(z,w) = f(z,w) g(-z,w), g2(z,w) = g(z,w) g(-z,w)
vvm f2, g2 = g;
rep(i, sz(g2)) if (i & 1) rep(j, sz(g2[i])) g2[i][j] *= -1;
f2 = convolution_2D(f, g2);
g2 = convolution_2D(g, g2);
// f3(z,w) = E(z,w) or O(z,w), g3(z,w) = e(z,w)
f.clear(); g.clear();
if (N & 1) rep(i, min<ll>(sz(f2) / 2, N / 2 + 1)) f.push_back(f2[2 * i + 1]);
else rep(i, min<ll>((sz(f2) + 1) / 2, N / 2 + 1)) f.push_back(f2[2 * i]);
rep(i, min<ll>((sz(g2) + 1) / 2, N / 2 + 1)) g.push_back(g2[2 * i]);
rep(i, sz(f)) if (sz(f[i]) > M + 1) f[i].resize(M + 1);
rep(i, sz(g)) if (sz(g[i]) > M + 1) g[i].resize(M + 1);
// N
N /= 2;
}
// N = 0 [z^0]g(z,w) = 1 [z^0]f(z,w)
f[0].resize(M + 1);
return f[0];
}
//O(N (log N)^2)
/*
* a(z) = Σi∈[0..n] a[i] z^i
* b(z) = Σi∈[1..n] b[i] z^i
* i∈[0..N] [z^N] a(z) b(z)^i
*
*
*/
vm coefficients_of_power(const vm& a, const vm& b, int N) {
// : https://noshi91.hatenablog.com/entry/2024/03/16/224034
// verify : https://judge.yosupo.jp/problem/compositional_inverse_of_formal_power_series_large
//
//
// [w^[0..N]] Σj∈[0..∞) ([z^N] a(z) b(z)^j) w^j
// = [z^N] [w^[0..N]] a(z) Σj∈[0..∞) (b(z) w)^j
// = [z^N] [w^[0..N]] a(z) / (1 - b(z)w)
// 2 -
int na = sz(a), nb = sz(b);
if (na == 0 || nb == 0) return vm(0, N + 1);
Assert(b[0] == 0);
vvm f(na, vm(1));
rep(i, na) f[i][0] = a[i];
vvm g(nb, vm(2));
g[0][0] = 1;
repi(i, 1, nb - 1) g[i][1] = -b[i];
return bostan_mori(f, g, N, N);
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
int n, m;
cin >> n >> m;
Factorial_mint fm(n + 10);
vm a(n + 1); mint pow_m1 = 1;
repi(i, 0, n) {
a[i] = fm.fact_inv(i) * pow_m1;
pow_m1 *= m + 1;
}
dump(a);
MFPS f(0, n + 1), g(0, n + 1);
repi(i, 0, n) f[i] = g[i] = fm.fact_inv(i);
f[0] = 0;
f /= g;
f.resize(n + 1);
dump(f);
vm c = coefficients_of_power(a, f.c, n);
// repi(i, 0, n) c[i] *= fm.fact(n);
dump(c);
c.push_back(0);
if (m + 2 < sz(c)) c[m + 2] = 0;
dump(c);
mint res = 0;
repi(i, 0, min(m + 1, n)) {
res += (c[i] - c[i + 1]) * i * i;
}
res *= fm.fact(n);
EXIT(res);
}
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