結果
問題 |
No.3228 Very Large Fibonacci Sum
|
ユーザー |
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提出日時 | 2025-08-12 15:17:20 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 7,460 bytes |
コンパイル時間 | 4,070 ms |
コンパイル使用メモリ | 287,040 KB |
実行使用メモリ | 6,272 KB |
最終ジャッジ日時 | 2025-08-12 15:17:26 |
合計ジャッジ時間 | 5,118 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 * 23 |
ソースコード
#include <bits/stdc++.h> using namespace std; using ll = long long; bool chmin(auto &a, auto b) { return a > b ? a = b, true : false; } bool chmax(auto &a, auto b) { return a < b ? a = b, true : false; } template<int MOD> struct modint { modint() : x(0) {} modint(long long v) { long long y = v % m(); if (y < 0) y += m(); x = (unsigned int)(y); } static modint raw(int v) { modint a; a.x = v; return a; } static constexpr int mod() { return m(); } unsigned int val() const { return x; } modint& operator++() { x++; if (x == m()) x = 0; return *this; } modint& operator--() { if (x == 0) x = m(); x--; return *this; } modint operator++(int) { modint res = *this; ++*this; return res; } modint operator--(int) { modint res = *this; --*this; return res; } modint& operator+=(const modint &r) { x += r.x; if (x >= m()) x -= m(); return *this; } modint& operator-=(const modint &r) { x -= r.x; if (x >= m()) x += m(); return *this; } modint& operator*=(const modint &r) { unsigned long long y = x; y *= r.x; x = (unsigned int)(y % m()); return *this; } modint &operator/=(const modint &r) { return *this = *this * r.inv(); } friend modint operator+(const modint &a, const modint &b) { return modint(a) += b; } friend modint operator-(const modint &a, const modint &b) { return modint(a) -= b; } friend modint operator*(const modint &a, const modint &b) { return modint(a) *= b; } friend modint operator/(const modint &a, const modint &b) { return modint(a) /= b; } friend bool operator==(const modint &a, const modint &b) { return a.x == b.x; } friend bool operator!=(const modint &a, const modint &b) { return a.x != b.x; } modint operator+() const { return *this; } modint operator-() const { return modint() - *this; } modint pow(long long k) const { assert(k >= 0); modint a = *this; modint res = 1; while (k > 0) { if (k & 1) res *= a; a *= a; k >>= 1; } return res; } modint inv() const { long long a = x, b = m(), 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 modint(u); } private: unsigned int x; static constexpr unsigned int m() { return MOD; } }; template<typename mint> struct matrix : vector<vector<mint>> { using vector<vector<mint>>::vector; matrix(int h, int w) : vector<vector<mint>>(h, vector<mint>(w)) {} matrix &operator*=(const mint &r) { for (vector<mint> &v : *this) { for (mint &a : v) a *= r; } return *this; } matrix &operator/=(const mint &r) { mint invr = r.inv(); return *this *= invr; } matrix &operator+=(const matrix& a) { assert(this->size() == a.size()); for (int i = 0; i < int(this->size()); i++) { assert((*this)[i].size() == a[i].size()); for (int j = 0; j < int((*this)[i].size()); j++) { (*this)[i][j] += a[i][j]; } } return *this; } matrix &operator-=(const matrix& a) { assert(this->size() == a.size()); for (int i = 0; i < int(this->size()); i++) { assert((*this)[i].size() == a[i].size()); for (int j = 0; j < int((*this)[i].size()); j++) { (*this)[i][j] -= a[i][j]; } } return *this; } matrix &operator*=(const matrix &a) { int n = this->size(), m = a.size(); assert(m >= 1); int l = a[0].size(); matrix res(n, vector<mint>(l)); for (int i = 0; i < n; i++) { assert(int((*this)[i].size()) == m); for (int k = 0; k < m; k++) { for (int j = 0; j < l; j++) { res[i][j] += (*this)[i][k] * a[k][j]; } } } return *this = res; } matrix operator*(const mint &r) const { return matrix(*this) *= r; } matrix operator/(const mint &r) const { return matrix(*this) /= r; } matrix operator+(const matrix &a) const { return matrix(*this) += a; } matrix operator-(const matrix &a) const { return matrix(*this) -= a; } matrix operator*(const matrix &a) const { return matrix(*this) *= a; } static constexpr matrix I(int n) { matrix res(n, n); for (int i = 0; i < n; i++) { res[i][i] = 1; } return res; } static constexpr matrix O(int n) { return matrix(n, n); } matrix pow(long long k) const { matrix res = I(this->size()), a = *this; while (k > 0) { if (k & 1) res *= a; a *= a; k >>= 1; } return res; } mint det() const { int n = this->size(); assert(n >= 1); assert((*this)[0].size() == this->size()); mint res = 1; matrix a = *this; for (int i = 0; i < n; i++) { for (int j = i; j < n; j++) { if (a[j][i] != 0) { if (i != j) res = -res; swap(a[i], a[j]); break; } } if (a[i][i] != 0) { for (int j = i + 1; j < n; j++) { mint inv = a[j][i] * a[i][i].inv(); for (int k = i + 1; k < n; k++) { a[j][k] -= a[i][k] * inv; } } } } for (int i = 0; i < n; i++) { res *= a[i][i]; } return res; } matrix inv() const { int n = this->size(); matrix a = *this, res = I(n); for (int i = 0; i < n; i++) { if (a[i][i] == 0) { for (int j = i + 1; j < n; j++) { if (a[j][i] != 0) { swap(a[i], a[j]); swap(res[i], res[j]); break; } } } assert(a[i][i] != 0); mint cef = a[i][i].inv(); for (int j = 0; j < n; j++) { a[i][j] *= cef; res[i][j] *= cef; } for (int j = 0; j < n; j++) { if (j != i) { cef = a[j][i]; for (int k = 0; k < n; k++) { a[j][k] -= a[i][k] * cef; res[j][k] -= res[i][k] * cef; } } } } return res; } }; using mint = modint<1000000007>; using Mat = matrix<mint>; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int a, b, c, e, d; cin >> a >> b >> c >> d >> e; Mat A = { {1, 1, 0, 0}, {0, c, d, e}, {0, 1, 0, 0}, {0, 0, 0, 1} }; ll N; cin >> N; A = A.pow(N); auto ans = A * Mat{ {a}, {b}, {a}, {1}, }; cout << ans[0][0].val() << endl; }