結果

問題 No.2801 Unique Maximum
ユーザー ecotteaecottea
提出日時 2024-07-02 18:34:16
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 3,637 ms / 4,000 ms
コード長 24,952 bytes
コンパイル時間 8,363 ms
コンパイル使用メモリ 352,496 KB
実行使用メモリ 185,820 KB
最終ジャッジ日時 2024-07-02 18:35:09
合計ジャッジ時間 49,139 ms
ジャッジサーバーID
(参考情報)
judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 21
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ソースコード

diff #
プレゼンテーションモードにする

// 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 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
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 >= 0; 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 = modint1000000007;
using mint = modint998244353;
//using mint = static_modint<999999017>;
//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) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
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(v)
#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
mint TLE(int n, int m) {
// dp[w][j] : w [0..j)
vvm dp(n + 1, vm(m + 1));
dp[0][0] = 1;
repi(w, 0, n) {
repi(j, 1, m) {
dp[w][j] += dp[w][j - 1];
rep(l, w) dp[w][j] += dp[l][j - 1] * dp[w - 1 - l][j - 1];
}
}
dumpel(dp);
return dp[n][m];
}
/*
0: 1 1 1 1 1 1 1 1 1 1 1
1: 0 1 2 3 4 5 6 7 8 9 10
2: 0 0 2 6 12 20 30 42 56 72 90
3: 0 0 1 9 30 70 135 231 364 540 765
4: 0 0 0 10 64 220 560 1190 2240 3864 6240
5: 0 0 0 8 118 630 2170 5810 13188 26628 49260
6: 0 0 0 4 188 1656 7916 27076 74760 177744 378312
7: 0 0 0 1 258 4014 27326 121023 409836 1153740 2836548
8: 0 0 0 0 302 8994 89582 520626 2179556 7303164 20817588
9: 0 0 0 0 298 18654 279622 2161158 11271436 45179508 149837028
10: 0 0 0 0 244 35832 832680 8674188 56788112 273613032 61067911
// https://oeis.org/A122888
// z → z+z^2 m [z^n]
*/
//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 (log N)^2)
/*
* FPS f(z), g(z)
* f(z) = Σi∈[0..n) f[i] z^i
* g(z) = Σj∈[1..m) g[j] z^j
* [z^[0..N)] f(g(z))
*
* mod 998244353
*/
vm composition(const vm& f, const vm& g, int N) {
// : https://qiita.com/ryuhe1/items/23d79bb84b270f7359e0
// verify : https://judge.yosupo.jp/problem/composition_of_formal_power_series_large
if (N == 0) return vm();
if (N == 1) return vm{ f[0] };
if (sz(g) == 0) {
vm res(N);
res[0] = f[0];
return res;
}
// 2^K : N 2
int K = msb(N - 1) + 1;
vvvm q(K);
q[0] = vvm(sz(g), vm(2));
q[0][0][0] = 1;
repi(i, 1, sz(g) - 1) q[0][i][1] = -g[i];
repi(k, 1, K - 1) {
auto q_pos(q[k - 1]);
int sz_q = sz(q[k - 1]);
for (int i = 1; i < sz_q; i += 2) rep(j, sz(q[k - 1][i])) q[k - 1][i][j] *= -1;
auto qk_dbl = convolution_2D(q_pos, q[k - 1]);
rep(i, min((sz(qk_dbl) + 1) / 2, (1 << (K - k)))) q[k].emplace_back(move(qk_dbl[2 * i]));
if (sz(q[k]) > N) q[k].resize(N);
}
int sz_q = sz(q[K - 1]);
for (int i = 1; i < sz_q; i += 2) rep(j, sz(q[K - 1][i])) q[K - 1][i][j] *= -1;
if (sz(q[K - 1]) > N) q[K - 1].resize(N);
vvm p(1, vm(N));
rep(i, min(sz(f), N)) p[0][N - 1 - i] = f[i];
auto tmp = convolution_2D(p, q[K - 1]);
int sz_p = min(2, sz(tmp));
p.resize(sz_p);
rep(i, sz_p) {
int j_min = N - (1 << (K - 1));
int j_max = min(N, sz(tmp[i])) - 1;
p[i].resize(j_max - j_min + 1);
repi(j, j_min, j_max) p[i][j - j_min] = tmp[i][j];
}
repir(k, K - 2, 0) {
vvm p_dbl(sz(p) * 2 - 1, vm(sz(p[0])));
rep(i, sz(p)) rep(j, sz(p[i])) p_dbl[i * 2][j] = p[i][j];
auto tmp = convolution_2D(p_dbl, q[k]);
int sz_p = min({ 1 << (K - k), N, sz(tmp) });
p.resize(sz_p);
rep(i, sz_p) {
int j_min = 1 << k;
int j_max = min(1 << (k + 1), sz(tmp[i])) - 1;
p[i].resize(j_max - j_min + 1);
repi(j, j_min, j_max) p[i][j - j_min] = tmp[i][j];
}
}
vm res(N);
rep(i, min(N, sz(p))) res[i] = p[i][0];
return res;
}
// O(n (log n)^2 log m)
mint TLE2(int n, int m) {
vm res{ 0, 1 }, pow2{ 0, 1, 1 };
while (m > 0) {
// dump(pow2);
if (m & 1) res = composition(res, pow2, n + 2);
pow2 = composition(pow2, pow2, n + 2);
m /= 2;
}
// dump(res);
return res[n + 1];
}
//mod 998244353
/*
* Online_convolution(int n) : O(n)
* a[0..n) b[0..n) c[0..n)
*
* set(mint a, mint b) : O((log n)^2)
* t a=a[t], b=b[t]
*
* reset() : O((log n)^2)
* set()
*
* mint [](int i) : O(1)
* c[i] = Σj∈[0..i] a[j] b[i-j]
* : a[0..i], b[0..i]
*
* mint back() : O(1)
* c[i]
*/
class Online_convolution {
// : https://qiita.com/Kiri8128/items/1738d5403764a0e26b4c
int n, t; // t :
vm as, bs, cs;
vector<pim> his;
public:
// n
Online_convolution(int n) : n(n), t(0), as(n), bs(n), cs(n) {
// verify : https://atcoder.jp/contests/abc280/tasks/abc280_e
}
Online_convolution() : n(0), t(0) {}
// t a=a[t], b=b[t]
void set(mint a, mint b) {
// verify : https://atcoder.jp/contests/abc280/tasks/abc280_e
as[t] = a; bs[t] = b;
int i1_max = lsb(t + 2), i2_max = i1_max;
//
if (popcount(t + 2) == 1) { i1_max -= 2; i2_max -= 1; }
// 2^i :
repi(i, 0, i1_max) {
// cs_sub[0..j_max]
int j_max = min((1 << (i + 1)) - 2, n - 1 - t);
// len :
int len = min(1 << i, j_max + 1);
// as[x_min..x_min+len) bs[y_min..y_min+len)
int x_min = t + 1 - (1 << i);
int y_min = (1 << i) - 1;
vm as_sub, bs_sub;
copy(as.begin() + x_min, as.begin() + (x_min + len), back_inserter(as_sub));
copy(bs.begin() + y_min, bs.begin() + (y_min + len), back_inserter(bs_sub));
vm cs_sub = convolution(as_sub, bs_sub);
repi(j, 0, j_max) {
cs[t + j] += cs_sub[j];
his.emplace_back(t + j, cs_sub[j]);
}
}
// 2^i :
repi(i, 0, i2_max) {
// cs_sub[0..j_max]
int j_max = min((1 << (i + 1)) - 2, n - 1 - t);
// len :
int len = min(1 << i, j_max + 1);
// as[x_min..x_min+len) bs[y_min..y_min+len)
int x_min = (1 << i) - 1;
int y_min = t + 1 - (1 << i);
vm as_sub, bs_sub;
copy(as.begin() + x_min, as.begin() + (x_min + len), back_inserter(as_sub));
copy(bs.begin() + y_min, bs.begin() + (y_min + len), back_inserter(bs_sub));
vm cs_sub = convolution(as_sub, bs_sub);
repi(j, 0, j_max) {
cs[t + j] += cs_sub[j];
his.emplace_back(t + j, cs_sub[j]);
}
}
t++;
}
// set()
void reset() {
t--;
int i1_max = lsb(t + 2), i2_max = i1_max;
if (popcount(t + 2) == 1) { i1_max -= 2; i2_max -= 1; }
repi(i, 0, i1_max) {
int j_max = min((1 << (i + 1)) - 2, n - 1 - t);
repi(j, 0, j_max) {
auto [pos, val] = his.back(); his.pop_back();
cs[pos] -= val;
}
}
repi(i, 0, i2_max) {
int j_max = min((1 << (i + 1)) - 2, n - 1 - t);
repi(j, 0, j_max) {
auto [pos, val] = his.back(); his.pop_back();
cs[pos] -= val;
}
}
as[t] = 0; bs[t] = 0;
}
// c[i]
mint const& operator[](int i) const {
// verify : https://atcoder.jp/contests/abc280/tasks/abc280_e
Assert(i < t);
return cs[i];
}
// c[i]
mint back() const {
// verify : https://judge.yosupo.jp/problem/log_of_formal_power_series
return cs[t - 1];
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Online_convolution& c) {
os << "a: " << c.as << endl;
os << "b: " << c.bs << endl;
os << "c: " << c.cs;
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];
}
};
Factorial_mint fm((int)2e5 + 10);
//mod 998244353
/*
* Online_composition(int n, mint g1, mint g2, Factorial_mint* fm) : O(n)
* g(z) = g1 z + g2 z^2 f(g(z)) [z^n]
* : fm n!
*
* set(mint a) : O((log n)^2)
* t a = [z^t]f(z)
*
* mint [](int i) : O(1)
* [z^i] f(g(z))
* : a[0..i]
*
* mint back() : O(1)
* f(g(z))
*/
class Online_composition {
int n, t; // t :
vm as;
vm g1_pow, g2_pow; vvm g_pow;
vvm fen; // f(g(z)) 1-indexed
vm cs;
vector<pim> his;
Factorial_mint* fm;
public:
// g(z) = g1 z + g2 z^2 f(g(z)) [z^n]
Online_composition(int n_, mint g1, mint g2, Factorial_mint* fm)
: n(1 << (msb(n_) + 1)), t(0), as(n), g1_pow(n), g2_pow(n), fen(n + 1), cs(n), fm(fm) {
int K = msb(n);
g1_pow[0] = 1;
g2_pow[0] = 1;
repi(i, 1, n - 1) {
g1_pow[i] = g1_pow[i - 1] * g1;
g2_pow[i] = g2_pow[i - 1] * g2;
}
g_pow.resize(K);
g_pow[0] = vm{ 0, g1, g2 };
repi(k, 1, K - 1) {
g_pow[k] = convolution(g_pow[k - 1], g_pow[k - 1]);
if (sz(g_pow[k]) > n) g_pow[k].resize(n);
}
}
Online_composition() : n(0), t(0), fm(nullptr) {}
// t a = [z^t]f(z)
void set(mint a) {
as[t] = a;
cs[t] += a * g1_pow[t];
int i = t + 1;
fen[i] = vm{ a };
int K = lsb(i);
rep(k, K) {
fen[i] = convolution(fen[i], g_pow[k]);
if (sz(fen[i]) > n) fen[i].resize(n);
int i2 = i - (1 << k);
rep(j, sz(fen[i2])) fen[i][j] += fen[i2][j];
}
if (i != n) {
int w = 1 << K;
int l = i - w;
// fen[i] g(z)^l cs[t+1..t+w]
// fen[i] z^[0..2(w-1)]
// g(z)^l z^[t+1-2(w-1)..t+w]
int W = 1 << (msb((t + w) - (t + 1 - 2 * (w - 1)) + 1 - 1) + 1);
mint W_inv = mint(W).inv();
vm fe(fen[i]);
fe.resize(W);
vm gl(W);
repi(j, t + 1 - 2 * (w - 1), t + w) {
int e2 = j - l;
if (e2 < 0) continue;
int e1 = l - e2;
if (e1 < 0) continue;
// [z^j]g(z)^l O(1)
gl[j - (t + 1 - 2 * (w - 1))] = g1_pow[e1] * g2_pow[e2] * fm->bin(l, e1);
}
internal::butterfly(fe);
internal::butterfly(gl);
rep(i, W) fe[i] *= gl[i];
internal::butterfly_inv(fe);
rep(j, w) {
mint val = fe[2 * (w - 1) + j] * W_inv;
cs[t + 1 + j] += val;
his.emplace_back(t + 1 + j, val);
}
}
t++;
}
// set()
void reset() {
t--;
int i = t + 1;
int K = lsb(i);
if (i != n) {
int w = 1 << K;
rep(j, w) {
auto [pos, val] = his.back(); his.pop_back();
cs[pos] -= val;
}
}
fen[i].clear();
cs[t] -= as[t] * g1_pow[t];
as[t] = 0;
}
// [z^i] f(g(z)) : a[0..i]
mint operator[](int i) const {
Assert(i < t);
return cs[i];
}
// f(g(z))
mint back() const {
return cs[t - 1];
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Online_composition& O) {
os << "f: " << O.as << endl;
os << "g: " << O.g_pow[0] << endl;
os << "h: " << O.cs << endl;
return os;
}
#endif
};
// O(n (log n)^2) n=200000 m=1000000000 5584 msreset() 使
mint TLE3(int n, int m) {
// dump("n, m:", n, m);
vm gm(n + 2);
gm[0] = 0;
gm[1] = 1;
gm[2] = m;
Online_convolution lhs(n + 4);
lhs.set(gm[0], gm[0] + 1);
lhs.set(gm[1], gm[1]);
lhs.set(gm[2], gm[2]);
Online_composition rhs(n + 4, 1, 1, &fm);
rhs.set(gm[0]);
rhs.set(gm[1]);
rhs.set(gm[2]);
// dump(lhs); dump(rhs);
repi(i, 3, n + 1) {
dump("---------- i:", i, "-----------");
lhs.set(0, 0);
lhs.set(0, 0);
rhs.set(0);
rhs.set(0);
dump(lhs); dump(rhs);
gm[i] = (lhs[i + 1] - rhs[i + 1]) * fm.inv(i - 2);
dump("gm[i]:", gm[i]);
lhs.reset();
lhs.reset();
rhs.reset();
rhs.reset();
dump(lhs); dump(rhs);
lhs.set(gm[i], gm[i]);
rhs.set(gm[i]);
dump(lhs); dump(rhs);
}
return gm[n + 1];
}
mint solve(int n, int m) {
// dump("n, m:", n, m);
vm gm(n + 2);
gm[0] = 0;
gm[1] = 1;
gm[2] = m;
Online_convolution lhs(n + 4);
lhs.set(gm[0], gm[0] + 1);
lhs.set(gm[1], gm[1]);
lhs.set(gm[2], gm[2]);
Online_composition rhs(n + 4, 1, 1, &fm);
rhs.set(gm[0]);
rhs.set(gm[1]);
rhs.set(gm[2]);
// dump(lhs); dump(rhs);
repi(i, 3, n + 1) {
dump("---------- i:", i, "-----------");
lhs.set(0, 0);
lhs.set(0, 0);
rhs.set(0);
rhs.set(0);
dump(lhs); dump(rhs);
gm[i] = (lhs[i + 1] - rhs[i + 1]) * fm.inv(i - 2);
dump("gm[i]:", gm[i]);
lhs.reset();
lhs.reset();
rhs.reset();
rhs.reset();
dump(lhs); dump(rhs);
lhs.set(gm[i], gm[i]);
rhs.set(gm[i]);
dump(lhs); dump(rhs);
}
return gm[n + 1];
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
// zikken();
int n, m;
cin >> n >> m;
cout << solve(n, m) << endl; dump("-----");
dump(TLE(n, m));
}
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