結果

問題 No.3228 Very Large Fibonacci Sum
ユーザー だれ
提出日時 2025-08-08 22:32:21
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 12,522 bytes
コンパイル時間 3,881 ms
コンパイル使用メモリ 228,900 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-08-08 22:32:26
合計ジャッジ時間 4,897 ms
ジャッジサーバーID
(参考情報)
judge1 / judge3
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 22 WA * 1
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 <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <unordered_set>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define _rep(i, n) _rep2(i, 0, n)
#define _rep2(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rep(...) GET_MACRO(__VA_ARGS__, _rep2, _rep)(__VA_ARGS__)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define UNIQUE(x)                      \
    std::sort((x).begin(), (x).end()); \
    (x).erase(std::unique((x).begin(), (x).end()), (x).end())
using i64 = long long;
using u64 = unsigned long long;
using u32 = unsigned int;
using i32 = int;
using ld = long double;
using f64 = double;
template <class T, class U>
bool chmin(T& a, const U& b) {
    return (b < a) ? (a = b, true) : false;
}
template <class T, class U>
bool chmax(T& a, const U& b) {
    return (b > a) ? (a = b, true) : false;
}
template <class T = std::string, class U = std::string>
inline void YesNo(bool f = 0, const T yes = "Yes", const U no = "No") {
    if (f)
        std::cout << yes << "\n";
    else
        std::cout << no << "\n";
}
namespace io {

template <class T, class U>
istream& operator>>(istream& i, pair<T, U>& p) {
    i >> p.first >> p.second;
    return i;
}

template <class T, class U>
ostream& operator<<(ostream& o, pair<T, U>& p) {
    o << p.first << " " << p.second;
    return o;
}

template <typename T>
istream& operator>>(istream& i, vector<T>& v) {
    rep(j, v.size()) i >> v[j];
    return i;
}
template <typename T>
string join(vector<T>& v) {
    stringstream s;
    rep(i, v.size()) s << ' ' << v[i];
    return s.str().substr(1);
}
template <typename T>
ostream& operator<<(ostream& o, vector<T>& v) {
    if (v.size()) o << join(v);
    return o;
}
template <typename T>
string join(vector<vector<T>>& vv) {
    string s = "\n";
    rep(i, vv.size()) s += join(vv[i]) + "\n";
    return s;
}
template <typename T>
ostream& operator<<(ostream& o, vector<vector<T>>& vv) {
    if (vv.size()) o << join(vv);
    return o;
}

void OUT() { std::cout << "\n"; }

template <class Head, class... Tail>
void OUT(Head&& head, Tail&&... tail) {
    std::cout << head;
    if (sizeof...(tail)) std::cout << ' ';
    OUT(std::forward<Tail>(tail)...);
}

void OUTL() { std::cout << std::endl; }

template <class Head, class... Tail>
void OUTL(Head&& head, Tail&&... tail) {
    std::cout << head;
    if (sizeof...(tail)) std::cout << ' ';
    OUTL(std::forward<Tail>(tail)...);
}

void IN() {}

template <class Head, class... Tail>
void IN(Head&& head, Tail&&... tail) {
    cin >> head;
    IN(std::forward<Tail>(tail)...);
}

}  // namespace io
using namespace io;

namespace useful {
long long modpow(long long a, long long b, long long mod) {
    long long res = 1;
    while (b) {
        if (b & 1) res *= a, res %= mod;
        a *= a;
        a %= mod;
        b >>= 1;
    }
    return res;
}

bool is_pow2(long long x) { return x > 0 && (x & (x - 1)) == 0; }

template <class T>
void rearrange(vector<T>& a, vector<int>& p) {
    vector<T> b = a;
    for (int i = 0; i < int(a.size()); i++) {
        a[i] = b[p[i]];
    }
    return;
}

template <std::forward_iterator I>
std::vector<std::pair<typename std::iterator_traits<I>::value_type, int>>
run_length_encoding(I s, I t) {
    if (s == t) return {};
    std::vector<std::pair<typename std::iterator_traits<I>::value_type, int>>
        res;
    res.emplace_back(*s, 1);
    for (auto it = ++s; it != t; it++) {
        if (*it == res.back().first)
            res.back().second++;
        else
            res.emplace_back(*it, 1);
    }
    return res;
}

vector<int> linear_sieve(int n) {
    vector<int> primes;
    vector<int> res(n + 1);
    iota(all(res), 0);
    for (int i = 2; i <= n; i++) {
        if (res[i] == i) primes.emplace_back(i);
        for (auto j : primes) {
            if (j * i > n) break;
            res[j * i] = j;
        }
    }
    return res;
    // return primes;
}

template <class T>
vector<long long> dijkstra(vector<vector<pair<int, T>>>& graph, int start) {
    int n = graph.size();
    vector<long long> res(n, 2e18);
    res[start] = 0;
    priority_queue<pair<long long, int>, vector<pair<long long, int>>,
                   greater<pair<long long, int>>>
        que;
    que.push({0, start});
    while (!que.empty()) {
        auto [c, v] = que.top();
        que.pop();
        if (res[v] < c) continue;
        for (auto [nxt, cost] : graph[v]) {
            auto x = c + cost;
            if (x < res[nxt]) {
                res[nxt] = x;
                que.push({x, nxt});
            }
        }
    }
    return res;
}

}  // namespace useful
using namespace useful;

template <class T, T l, T r>
struct RandomIntGenerator {
    std::random_device seed;
    std::mt19937_64 engine;
    std::uniform_int_distribution<T> uid;

    RandomIntGenerator() {
        engine = std::mt19937_64(seed());
        uid = std::uniform_int_distribution<T>(l, r);
    }

    T gen() { return uid(engine); }
};

#include <algorithm>
#include <atcoder/modint>
#include <cassert>
#include <iostream>
#include <utility>
#include <vector>

template <class R>
struct Matrix {
    int H, W;
    std::vector<std::vector<R>> A;

    Matrix(int h, int w) : H(h), W(w), A(std::vector(h, std::vector<R>(w))) {}
    Matrix(int n) : Matrix(n, n) {}
    Matrix(const std::vector<std::vector<R>>& a)
        : H(a.size()), W(a[0].size()), A(a) {}

    inline const std::vector<R>& operator[](int i) const { return A[i]; }

    inline std::vector<R>& operator[](int i) { return A[i]; }

    void swap_row(int i, int j) { std::swap(A[i], A[j]); }

    void swap_column(int i, int j) {
        for (int k = 0; k < H; k++) {
            std::swap(A[k][i], A[k][j]);
        }
    }

    Matrix& operator+=(const Matrix& B) {
        assert(H == B.H && W == B.W);
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) {
                A[i][j] += B[i][j];
            }
        }
        return *this;
    }

    Matrix& operator-=(const Matrix& B) {
        assert(H == B.H && W == B.W);
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) {
                A[i][j] += B[i][j];
            }
        }
        return *this;
    }

    Matrix& operator*=(const Matrix& B) {
        assert(W == B.H);
        std::vector C(H, std::vector<R>(B.W, R(0)));
        for (int i = 0; i < H; i++) {
            for (int k = 0; k < W; k++) {
                for (int j = 0; j < B.W; j++) {
                    C[i][j] += A[i][k] * B[k][j];
                }
            }
        }
        A.swap(C);
        W = B.W;
        return (*this);
    }

    Matrix operator+(const Matrix& B) const { return Matrix(*this) += B; }

    Matrix operator-(const Matrix& B) const { return Matrix(*this) -= B; }

    Matrix operator*(const Matrix& B) const { return Matrix(*this) *= B; }

    bool operator==(const Matrix& B) const {
        if (H != B.H || W != B.W) return false;
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) {
                if (A[i][j] != B[i][j]) return false;
            }
        }
        return true;
    }

    friend std::ostream& operator<<(std::ostream& os, const Matrix& B) {
        for (int i = 0; i < B.H; i++) {
            for (int j = 0; j < B.W; j++) {
                os << B[i][j] << (j == B.W - 1 ? "\n" : " ");
            }
        }
        return os;
    }

    // return {rank, det}
    static std::pair<int, R> GaussElimination(Matrix& a, int pivot_end = -1,
                                              bool diagonalize = false) {
        int h = a.H, w = a.W, rank = 0;
        if (pivot_end == -1) pivot_end = w;
        R det = 1;
        for (int j = 0; j < pivot_end; j++) {
            int idx = -1;
            for (int i = rank; i < h; i++) {
                if (a[i][j] != R(0)) {
                    idx = i;
                    break;
                }
            }
            if (idx == -1) {
                det = 0;
                continue;
            }
            if (rank != idx) {
                det = -det;
                a.swap_row(rank, idx);
            }
            det *= a[rank][j];
            if (diagonalize && a[rank][j] != R(1)) {
                R cr = R(1) / a[rank][j];
                for (int k = j; k < w; k++) a[rank][k] *= cr;
            }
            int is = diagonalize ? 0 : rank + 1;
            for (int i = is; i < h; i++) {
                if (i == rank) continue;
                if (a[i][j] != R(0)) {
                    R cr = a[i][j] / a[rank][j];
                    for (int k = j; k < w; k++) a[i][k] -= a[rank][k] * cr;
                }
            }
            rank++;
        }
        return std::make_pair(rank, det);
    }

    std::pair<std::vector<R>, std::vector<std::vector<R>>> LinearEquation(
        std::vector<R> b) {
        assert(H == (int)b.size());
        Matrix<R> M = Matrix(*this);
        for (int i = 0; i < H; i++) M[i].push_back(b[i]);
        M.W++;
        auto [rank, _] = Matrix<R>::GaussElimination(M, W, true);
        for (int i = rank; i < H; i++) {
            if (M[i][W] != R(0))
                return std::make_pair(std::vector<R>(),
                                      std::vector<std::vector<R>>());
        }
        std::vector<R> sol(W, 0);
        std::vector<std::vector<R>> basis;
        std::vector<int> pivot(W, -1);
        for (int i = 0, j = 0; i < rank; i++) {
            while (M[i][j] == R(0)) j++;
            sol[j] = M[i][W], pivot[j] = i;
        }
        for (int j = 0; j < W; j++) {
            if (pivot[j] == -1) {
                std::vector<R> x(W);
                x[j] = 1;
                for (int k = 0; k < j; k++) {
                    if (pivot[k] != -1) x[k] = -M[pivot[k]][j];
                }
                basis.emplace_back(x);
            }
        }
        return std::make_pair(sol, basis);
    }
};

template <class R>
struct SquareMatrix : Matrix<R> {
    int N;

    SquareMatrix(int n_) : Matrix<R>(n_, n_), N(n_) {}

    SquareMatrix<R> inverse() const {
        Matrix<R> m(N, 2 * N);
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                m[i][j] = this->A[i][j];
            }
            m[i][N + i] = R(1);
        }
        auto [rank, det] = Matrix<R>::GaussElimination(m, N, true);
        if (rank != N) return SquareMatrix<R>(0);

        SquareMatrix<R> res(N);
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                res[i][j] = m[i][N + j];
            }
        }
        return res;
    }

    R determinant() {
        Matrix M = Matrix(*this);
        auto [rank, det] = Matrix<R>::GaussElimination(M);
        return det;
    }

    static SquareMatrix<R> I(int n) {
        SquareMatrix<R> res(n);
        for (int i = 0; i < n; i++) res[i][i] = R(1);
        return res;
    }

    SquareMatrix<R> pow(unsigned long long x) {
        SquareMatrix<R> res = SquareMatrix<R>::I(N);
        auto a = SquareMatrix(*this);
        while (x > 0) {
            if (x & 1) res *= a;
            a *= a;
            x >>= 1;
        }
        return res;
    }

    R cofactor(int x, int y) {
        SquareMatrix<R> a(N - 1);
        for (int i = 0; i < N; i++) {
            if (i == x) continue;
            for (int j = 0; j < N; j++) {
                if (j == y) continue;
                a[i - (i > x)][j - (j > y)] = this->A[i][j];
            }
        }
        R res = a.determinant();
        if ((x + y) & 1) res = -res;
        return res;
    }
};

using mint = atcoder::modint1000000007;

int main() {
    std::cout << fixed << setprecision(15);
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    i64 a, b, c, d, e, n;
    IN(a, b, c, d, e, n);
    if (n == 0) {
        OUT(a);
        return 0;
    }
    Matrix<mint> x0(4, 1);
    x0[0][0] = b;
    x0[1][0] = a;
    x0[2][0] = 1;
    x0[3][0] = a + b;
    SquareMatrix<mint> M(4);
    M[0][0] = M[3][0] = c;
    M[0][1] = M[3][1] = d;
    M[0][2] = M[3][2] = e;
    M[1][0] = M[2][2] = M[3][3] = 1;
    M = M.pow(n - 1);
    auto y = M * x0;
    OUT(y[3][0].val());
}
0