結果
| 問題 | No.2413 Multiple of 99 |
| ユーザー |
 KumaTachiRen
|
| 提出日時 | 2023-08-11 23:47:51 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 8,766 bytes |
| コンパイル時間 | 9,932 ms |
| コンパイル使用メモリ | 356,496 KB |
| 実行使用メモリ | 110,788 KB |
| 最終ジャッジ日時 | 2024-11-18 19:35:28 |
| 合計ジャッジ時間 | 128,325 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 14 TLE * 7 |
ソースコード
#pragma GCC target("avx2")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#include <bits/stdc++.h>#include <atcoder/all>using namespace std;using namespace atcoder;struct Fast {Fast() {std::cin.tie(nullptr);ios::sync_with_stdio(false);cout << setprecision(10);}} fast;#define popcount(x) __builtin_popcount(x)#define all(a) (a).begin(), (a).end()#define contains(a, x) ((a).find(x) != (a).end())#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (a); i--)#define writejoin(s, a) rep(_i, 0, (a).size()) cout << (a)[_i] << (_i + 1 < (int)(a).size() ? s : "\n");#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";#define yn(b) cout << ((b) ? "yes" : "no") << "\n";using ll = long long;using mint = modint998244353;template <typename mint>class Factorial {public:Factorial(int max) : n(max) {f = vector<mint>(n + 1);finv = vector<mint>(n + 1);f[0] = 1;for (int i = 1; i <= n; i++) f[i] = f[i - 1] * i;finv[n] = f[n].inv();for (int i = n; i > 0; i--) finv[i - 1] = finv[i] * i;}mint fact(int k) {assert(0 <= k && k <= n);return f[k];}mint fact_inv(int k) {assert(0 <= k && k <= n);return finv[k];}mint binom(int k, int r) {assert(0 <= k && k <= n);if (r < 0 || r > k) return 0;return f[k] * finv[r] * finv[k - r];}mint inv(int k) {assert(0 < k && k <= n);return finv[k] * f[k - 1];}private:int n;vector<mint> f, finv;};template <typename mint>struct 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 mint &v) {for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;return *this;}FPS &operator*=(const FPS &r) {auto c = convolution<mint>((*this), r);this->resize(c.size());for (int i = 0; i < (int)c.size(); i++) (*this)[i] = c[i];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.at(g.size() - 1).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(begin(ret), end(ret));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(begin(*this), begin(*this) + 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::get_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)[0] == mint(0));if (deg == -1) deg = (*this).size();FPS ret{mint(1)};for (int i = 1; i < deg; i <<= 1)ret = (ret * ((*this).pre(i << 1) - ret.log(i << 1) + 1)).pre(i << 1);return ret.pre(deg);}};vector<mint> mul(const vector<mint> &f, const vector<mint> &g) {auto h = convolution(f, g);rrep(i, 99, h.size()) h[i - 99] += h[i];if ((int)h.size() > 99) h.resize(99);return h;}using fps = FormalPowerSeries<mint>;int main() {int n, k;cin >> n >> k;Factorial<mint> fact(2000000);int mf = n / 2;fps f;{fps fp = fps(mf * 10 + 1, 0);fps fq = fps(mf + 1, 0);rep(i, 0, mf + 1) {fq[i] = fact.binom(mf, i);if (i % 2 == 1) {fq[i] = -fq[i];}fp[i * 10] = fq[i];}f = fp * fq.inv(mf * 9 + 1);f.resize(mf * 9 + 1);}fps g(f.size());rep(i, 0, f.size()) g[i] = f[i];if (n & 1) g *= fps(10, 1);f.resize(g.size());vector<fps> fr(99), gr(99);queue<fps> qf, qg, qh;rep(r, 0, 99) {if (r >= (int)g.size()) {fr[r] = fps{};gr[r] = fps{};} else {for (int v = r; v < (int)g.size(); v += 99) {qf.push(fps{f[v]});qg.push(fps{g[v]});qh.push(fps{1, -v});}while (qf.size() > 1) {auto f1 = qf.front();qf.pop();auto f2 = qf.front();qf.pop();auto g1 = qg.front();qg.pop();auto g2 = qg.front();qg.pop();auto h1 = qh.front();qh.pop();auto h2 = qh.front();qh.pop();qf.push(f1 * h2 + f2 * h1);qg.push(g1 * h2 + g2 * h1);qh.push(h1 * h2);}auto h = qh.front().inv(k + 1);fr[r] = qf.front() * h;gr[r] = qg.front() * h;qf.pop();qg.pop();qh.pop();}}mint ans = 0;rep(v, 0, 99) {int w = (99 - v) * 10 % 99;auto frr = fr[v];auto grr = gr[w];rep(i, 0, fr[v].size()) {int j = k - i;if (j < (int)gr[w].size()) ans += fact.binom(k, i) * frr[i] * grr[j];}}cout << ans.val() << "\n";}