結果

問題 No.3228 Very Large Fibonacci Sum
ユーザー nonon
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
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 * 23
権限があれば一括ダウンロードができます

ソースコード

diff #

#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;
}
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