Educational Codeforces Round 13 D. Iterated Linear Function (矩阵快速幂)

题目链接：http://codeforces.com/problemset/problem/678/D

简单的矩阵快速幂模版题

矩阵是这样的：

#include <bits/stdc++.h>
using namespace std;
typedef __int64 LL;
struct data {
    LL mat[3][3];
};
LL mod = 1e9 + 7;

data operator *(data a , data b) {
    data res;
    for(int i = 1 ; i <= 2 ; ++i) {
        for(int j = 1 ; j <= 2 ; ++j) {
            res.mat[i][j] = 0;
            for(int k = 1 ; k <= 2 ; ++k) {
                res.mat[i][j] = (a.mat[i][k] * b.mat[k][j] % mod + res.mat[i][j]) % mod;
            }
        }
    }
    return res;
}

data operator ^(data a , LL n) {
    data res;
    for(int i = 1 ; i <= 2 ; ++i) {
        for(int j = 1 ; j <= 2 ; ++j) {
            res.mat[i][j] = i == j;
        }
    }
    while(n) {
        if(n & 1)
            res = res * a;
        a = a * a;
        n >>= 1;
    }
    return res;
}

int main()
{
    LL a , b , n , x;
    cin >> a >> b >> n >> x;
    data temp , res;
    temp.mat[1][1] = a % mod , temp.mat[1][2] = 0 , temp.mat[2][1] = b % mod, temp.mat[2][2] = 1;
    res.mat[1][1] = x % mod , res.mat[1][2] = 1 , res.mat[2][1] = res.mat[2][2] = 0;
    temp = temp ^ n;
    res = res * temp;
    cout << res.mat[1][1] << endl;
    return 0;
}