結果
問題 | No.2511 Mountain Sequence |
ユーザー |
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提出日時 | 2023-10-20 22:08:15 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 6,097 bytes |
コンパイル時間 | 5,276 ms |
コンパイル使用メモリ | 275,944 KB |
最終ジャッジ日時 | 2025-02-17 09:34:58 |
ジャッジサーバーID (参考情報) |
judge3 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | WA * 3 |
other | WA * 32 |
ソースコード
#include <stdio.h>#include <atcoder/all>#include <bits/stdc++.h>using namespace std;using namespace atcoder;using mint = modint998244353;#define rep(i,n) for (int i = 0; i < (n); ++i)#define Inf32 1000000001#define Inf64 4000000000000000001struct combi{deque<mint> kaijou;deque<mint> kaijou_;combi(int n){kaijou.push_back(1);for(int i=1;i<=n;i++){kaijou.push_back(kaijou[i-1]*i);}mint b=kaijou[n].inv();kaijou_.push_front(b);for(int i=1;i<=n;i++){int k=n+1-i;kaijou_.push_front(kaijou_[0]*k);}}mint combination(int n,int r){if(r>n)return 0;mint a = kaijou[n]*kaijou_[r];a *= kaijou_[n-r];return a;}mint junretsu(int a,int b){mint x = kaijou_[a]*kaijou_[b];x *= kaijou[a+b];return x;}mint catalan(int n){return combination(2*n,n)/(n+1);}};combi C(500000);// https://nyaannyaan.github.io/library/fps/formal-power-series.hppstruct FormalPowerSeries : vector<mint> {using vector<mint>::vector;using FPS = FormalPowerSeries;FPS &operator+=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];return *this;}FPS &operator+=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] += r;return *this;}FPS &operator-=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];return *this;}FPS &operator-=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] -= r;return *this;}FPS &operator*=(const FPS &r) {auto ret = convolution(r,*this);return (*this) = FPS(ret.begin(),ret.end());}FPS &operator*=(const mint &v) {for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;return *this;}FPS &operator/=(const FPS &r) {if (this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;if ((int)r.size() <= 64) {FPS f(*this), g(r);g.shrink();mint coeff = g.back().inv();for (auto &x : g) x *= coeff;int deg = (int)f.size() - (int)g.size() + 1;int gs = g.size();FPS quo(deg);for (int i = deg - 1; i >= 0; i--) {quo[i] = f[i + gs - 1];for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];}*this = quo * coeff;this->resize(n, mint(0));return *this;}return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();}FPS &operator%=(const FPS &r) {*this -= *this / r * r;shrink();return *this;}FPS operator+(const FPS &r) const { return FPS(*this) += r; }FPS operator+(const mint &v) const { return FPS(*this) += v; }FPS operator-(const FPS &r) const { return FPS(*this) -= r; }FPS operator-(const mint &v) const { return FPS(*this) -= v; }FPS operator*(const FPS &r) const { return FPS(*this) *= r; }FPS operator*(const mint &v) const { return FPS(*this) *= v; }FPS operator/(const FPS &r) const { return FPS(*this) /= r; }FPS operator%(const FPS &r) const { return FPS(*this) %= r; }FPS operator-() const {FPS ret(this->size());for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];return ret;}void shrink() {while (this->size() && this->back() == mint(0)) this->pop_back();}FPS rev() const {FPS ret(*this);reverse(ret.begin(), ret.end());return ret;}FPS dot(FPS r) const {FPS ret(min(this->size(), r.size()));for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];return ret;}FPS pre(int sz) const {return FPS((*this).begin(), (*this).begin() + min((int)this->size(), sz));}FPS operator>>(int sz) const {if ((int)this->size() <= sz) return {};FPS ret(*this);ret.erase(ret.begin(), ret.begin() + sz);return ret;}FPS operator<<(int sz) const {FPS ret(*this);ret.insert(ret.begin(), sz, mint(0));return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));mint one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {const int n = (int)this->size();FPS ret(n + 1);ret[0] = mint(0);if (n > 0) ret[1] = mint(1);auto mod = mint::mod();for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];return ret;}mint eval(mint x) const {mint r = 0, w = 1;for (auto &v : *this) r += w * v, w *= x;return r;}FPS log(int deg = -1) const {assert((*this)[0] == mint(1));if (deg == -1) deg = (int)this->size();return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}FPS pow(int64_t k, int deg = -1) const {const int n = (int)this->size();if (deg == -1) deg = n;if (k == 0) {FPS ret(deg);if (deg) ret[0] = 1;return ret;}for (int i = 0; i < n; i++) {if ((*this)[i] != mint(0)) {mint rev = mint(1) / (*this)[i];FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);ret *= (*this)[i].pow(k);ret = (ret << (i * k)).pre(deg);if ((int)ret.size() < deg) ret.resize(deg, mint(0));return ret;}if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));}return FPS(deg, mint(0));}FPS inv(int deg = -1) const {assert((*this)[0] != mint(0));if (deg == -1) deg = (*this).size();FPS ret({mint(1) / (*this)[0]});for (int i = 1; i < deg; i <<= 1)ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1);return ret.pre(deg);}FPS exp(int deg = -1) const{assert((*this).size() == 0 || (*this)[0] == mint(0));if (deg == -1) deg = (int)this->size();FPS ret({mint(1)});for (int i = 1; i < deg; i <<= 1) {ret = (ret * (pre(i << 1) + mint(1) - ret.log(i << 1))).pre(i << 1);}return ret.pre(deg);}};using fps = FormalPowerSeries;//?int main(){int N,M;cin>>N>>M;fps f({1,2,1});f = f.pow(M,N+5);f *= -1;f[0]++;f *= fps({-1,-1}).inv(N+5);while(f.size()<N+5)f.push_back(0);cout<<f[N-1].val()<<endl;return 0;}