結果
問題 | No.2883 K-powered Sum of Fibonacci |
ユーザー | nonon |
提出日時 | 2024-09-08 21:30:53 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 6 ms / 3,000 ms |
コード長 | 10,136 bytes |
コンパイル時間 | 2,948 ms |
コンパイル使用メモリ | 224,264 KB |
実行使用メモリ | 6,944 KB |
最終ジャッジ日時 | 2024-09-08 21:30:58 |
合計ジャッジ時間 | 4,501 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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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
6,812 KB |
testcase_01 | AC | 2 ms
6,940 KB |
testcase_02 | AC | 2 ms
6,944 KB |
testcase_03 | AC | 2 ms
6,940 KB |
testcase_04 | AC | 2 ms
6,940 KB |
testcase_05 | AC | 3 ms
6,944 KB |
testcase_06 | AC | 2 ms
6,940 KB |
testcase_07 | AC | 3 ms
6,944 KB |
testcase_08 | AC | 3 ms
6,944 KB |
testcase_09 | AC | 3 ms
6,940 KB |
testcase_10 | AC | 3 ms
6,944 KB |
testcase_11 | AC | 5 ms
6,944 KB |
testcase_12 | AC | 4 ms
6,944 KB |
testcase_13 | AC | 3 ms
6,944 KB |
testcase_14 | AC | 5 ms
6,940 KB |
testcase_15 | AC | 3 ms
6,944 KB |
testcase_16 | AC | 2 ms
6,944 KB |
testcase_17 | AC | 3 ms
6,944 KB |
testcase_18 | AC | 3 ms
6,944 KB |
testcase_19 | AC | 3 ms
6,940 KB |
testcase_20 | AC | 5 ms
6,944 KB |
testcase_21 | AC | 5 ms
6,940 KB |
testcase_22 | AC | 6 ms
6,944 KB |
testcase_23 | AC | 5 ms
6,944 KB |
testcase_24 | AC | 5 ms
6,940 KB |
testcase_25 | AC | 5 ms
6,944 KB |
testcase_26 | AC | 5 ms
6,940 KB |
testcase_27 | AC | 5 ms
6,944 KB |
testcase_28 | AC | 5 ms
6,944 KB |
testcase_29 | AC | 5 ms
6,940 KB |
testcase_30 | AC | 2 ms
6,940 KB |
testcase_31 | AC | 2 ms
6,940 KB |
testcase_32 | AC | 2 ms
6,944 KB |
testcase_33 | AC | 2 ms
6,944 KB |
testcase_34 | AC | 2 ms
6,940 KB |
testcase_35 | AC | 2 ms
6,940 KB |
testcase_36 | AC | 2 ms
6,940 KB |
testcase_37 | AC | 2 ms
6,940 KB |
testcase_38 | AC | 2 ms
6,940 KB |
testcase_39 | AC | 2 ms
6,940 KB |
testcase_40 | AC | 2 ms
6,944 KB |
testcase_41 | AC | 2 ms
6,940 KB |
testcase_42 | AC | 5 ms
6,940 KB |
ソースコード
#include <bits/stdc++.h> using namespace std; template<long long MOD> struct modint { modint() : x(0) {} modint(long long v) : x(v % MOD) { if (x < 0) x += MOD; } long long x; long long val() const { return x; } static constexpr long long mod() noexcept { return MOD; } friend modint operator+(modint a, modint b) { return a.x + b.x; } friend modint operator-(modint a, modint b) { return a.x - b.x; } friend modint operator*(modint a, modint b) { return a.x * b.x; } friend modint operator/(modint a, modint b) { return a.x * b.inv(); } friend modint operator+=(modint &a, modint b) { return a = a + b; } friend modint operator-=(modint &a, modint b) { return a = a - b; } friend modint operator*=(modint &a, modint b) { return a = a * b; } friend modint operator/=(modint &a, modint b) { return a = a / b; } friend bool operator==(modint a, modint b) {return a.x == b.x; } friend bool operator!=(modint a, modint b) {return a.x != b.x; } modint operator+() const { return *this; } modint operator-() const { return modint() - *this; } modint pow(long long k) const { modint a = x, res = 1; while (k > 0) { if (k & 1) res *= a; a *= a; k >>= 1; } return res; } modint inv() const { long long a = x, b = MOD; long long u = 1, v = 0; while (b > 0) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } return u; } modint& operator++() { x++; if (x == MOD ) x = 0; return *this; } modint& operator--() { if (x == 0) x = MOD; x--; return *this; } modint operator++(int) { modint res = *this; ++*this; return res; } modint operator--(int) { modint res = *this; --*this; return res; } }; template<typename mint> void ntt(vector<mint> &f, bool inv = false) { const int mod = mint::mod(); int n = f.size(); mint r = 3; // mod が 998244353 でないなら適切に変更すること if (inv) r = r.inv(); vector<mint> g(n); for (int i = n / 2; i > 0; i >>= 1) { mint z = r.pow( (mod - 1) / (n / i) ); mint w = 1; for (int j = 0; j < n; j += i << 1) { for (int k = 0; k < i; k++) { f[i + j + k] *= w; g[0 / 2 + j / 2 + k] = f[j + k] + f[i + j + k]; g[n / 2 + j / 2 + k] = f[j + k] - f[i + j + k]; } w *= z; } swap(f, g); } if (inv) { mint inv = mint(n).inv(); for (mint &a : f) a *= inv; } } template<typename mint> vector<mint> convolution(vector<mint> f, vector<mint> g, int d = -1) { int n = f.size(), m = g.size(); if (n == 0 || m == 0) return {}; int sz = 1; while (sz < n + m - 1) sz <<= 1; f.resize(sz); ntt(f); g.resize(sz); ntt(g); for (int i = 0; i < sz; i++) f[i] *= g[i]; ntt(f, true); if (d == -1) d = n + m - 1; f.resize(d); return f; } #include <cassert> template<typename mint> struct Formal_Power_Series : vector<mint> { using FPS = Formal_Power_Series; using vector<mint>::vector; FPS& operator*=(mint r) { for (mint &x : *this) x *= r; return *this; } FPS& operator/=(mint r) { mint invr = r.inv(); (*this) *= invr; return *this; } FPS operator*(mint r) const { return FPS(*this) *= r; } FPS operator/(mint r) const { return FPS(*this) /= r; } FPS& operator+=(const FPS &f) { if (this->size() < f.size()) this->resize(f.size()); for (int i = 0; i < f.size(); i++) (*this)[i] += f[i]; return *this; } FPS& operator-=(const FPS &f) { if (this->size() < f.size()) this->resize(f.size()); for (int i = 0; i < f.size(); i++) (*this)[i] -= f[i]; return *this; } FPS& operator*=(const FPS &f) { vector<mint> s(this->begin(), this->end()); vector<mint> t(f.begin(), f.end()); s = convolution(s, t); this->resize(s.size()); for (int i = 0; i < s.size(); i++) { (*this)[i] = s[i]; } return *this; } FPS& operator/=(const FPS &f) { *this *= f.inv(); return *this; } FPS& operator%=(const FPS& f) { *this -= this->div(f) * f; this->shrink(); return *this; } FPS operator+(const FPS &f) const { return FPS(*this) += f; } FPS operator-(const FPS &f) const { return FPS(*this) -= f; } FPS operator*(const FPS &f) const { return FPS(*this) *= f; } FPS operator/(const FPS &f) const { return FPS(*this) /= f; } FPS operator%(const FPS &f) const { return FPS(*this) %= f; } FPS operator-() const { return FPS{} - *this; } FPS div(FPS f) { if (this->size() < f.size()) return FPS{}; int n = this->size() - f.size() + 1; return (rev().pre(n) * f.rev().inv()).pre(n).rev(n); } FPS pre(int n) { n = min(n, int(this->size())); return FPS(this->begin(), this->begin() + n); } FPS rev(int n = -1) { FPS f(*this); if (n != -1) f.resize(n); reverse(f.begin(), f.end()); return f; } void shrink() { while (this->size() && this->back() == mint(0)) { this->pop_back(); } } FPS dot(FPS f) { int n = min(this->size(), f.size()); FPS g(n); for (int i = 0; i < n; i++) { g[i] = (*this)[i] * f[i]; } return g; } FPS diff() { int n = this->size(); if (n == 0) return FPS{}; FPS f(n - 1); for (int i = 1; i < n; i++) { f[i - 1] = (*this)[i] * i; } return f; } FPS integral() { int n = this->size(); FPS f(n + 1); for (int i = 0; i < n; i++) { f[i + 1] = (*this)[i] / (i + 1); } return f; } FPS inv() { int n = this->size(); FPS f(n); f[0] = (*this)[0].inv(); for (int d = 1; d < n; d *= 2) { FPS s(2 * d), t(2 * d); for (int i = 0; i < min(n, 2 * d); i++) s[i] = (*this)[i]; for (int i = 0; i < d; i++) t[i] = f[i]; ntt(s); ntt(t); s = s.dot(t); ntt(s, true); for (int i = 0; i < d; i++) s[i] = 0; ntt(s); s = s.dot(t); ntt(s, true); for (int i = d; i < min(n, 2 * d); i++) f[i] -= s[i]; } return f; } FPS exp() { int n = this->size(); FPS f(1, 1); for (int d = 1; d < n; d *= 2) { FPS g = pre(2 * d); g[0] += 1; f.resize(2 * d); g -= f.log(); f *= g; f.resize(2 * d); } f.resize(n); return f; } FPS log() { int n = this->size(); return (diff() * inv()).pre(n - 1).integral(); } FPS pow(long long k) { int n = this->size(); if (k == 0) { FPS f(n, 0); f[0] = 1; return f; } int c = 0; while (c < n && (*this)[c] == 0) c++; if (c > (n - 1) / k) return FPS(n, 0); FPS f(*this); for (int i = 0; i + c < n; i++) f[i] = (*this)[i + c]; f = ((f / f[0]).log() * k).exp() * f[0].pow(k); FPS g(n); for (int i = 0; i + k * c < n; i++) g[i + k * c] = f[i]; return g; } }; using mint = modint<998244353>; using FPS = Formal_Power_Series<mint>; vector<mint> Berlekamp_Massey(const vector<mint> &a) { int n = a.size(); vector<mint> b = {1}, c = {1}; mint y = 1; for (int d = 1; d <= n; d++) { int k = b.size(), l = c.size(); mint x = 0; for (int i = 0; i < l; i++) { x += c[i] * a[d - l + i]; } b.push_back(0); k++; if (x == 0) continue; mint buf = x / y; if (l < k) { vector<mint> tmp = c; c.insert(c.begin(), k - l, 0); for (int i = 0; i < k; i++) { c[k - i - 1] -= buf * b[k - i -1]; } b = tmp; y = x; } else { for (int i = 0; i < k; i++) { c[l - i - 1] -= buf * b[k - i - 1]; } } } reverse(c.begin(), c.end()); for (mint &x : c) x = -x; return c; } mint Bostan_Mori(FPS p, FPS q, long long k) { mint res = 0; if (p.size() >= q.size()) { FPS r = p.div(q); p -= q * r; p.shrink(); if (k < r.size()) res += r[k]; } if (p.empty()) return res; p.resize( q.size() - 1 ); auto sub = [&](const FPS &f, bool odd = 0) -> FPS { int n = f.size(); if (!odd) n++; FPS g(n / 2); for (int i = odd; i < f.size(); i += 2) g[i / 2] = f[i]; return g; }; while (k) { FPS q2 = q; for (int i = 1; i < q2.size(); i += 2) q2[i] = -q2[i]; p = sub(p * q2, k & 1); q = sub(q * q2); k /= 2; } return res + p[0]; } mint linear_recurrence(FPS a, FPS c, long long k) { FPS c2(c.size() + 1); for (int i = 0; i < c.size(); i++) c2[i + 1] = -c[i]; c2[0] = 1; return Bostan_Mori((a * c2).pre(a.size()), c2, k); } mint BMBM(vector<mint> x, long long k) { auto tmp = Berlekamp_Massey(x); int n = tmp.size() - 1; FPS a(n), c(n); for (int i = 0; i < n; i++) { a[i] = x[i]; c[i] = tmp[i + 1]; } return linear_recurrence(a, c, k); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); long long N; int K; cin >> N >> K; int M = 4 * K; vector<mint> F(M), A(M); F[0] = F[1] = 1; A[0] = 1, A[1] = 2; for (int i = 2; i < M; i++) { F[i] = F[i - 1] + F[i - 2]; A[i] = A[i - 1] + F[i].pow(K); } cout << BMBM(A, N - 1).val() << endl; }