Problem 3: Matrix Exponentiation for Fibonacci Numbers

Problem Statement: Compute the n-th Fibonacci number modulo 10^9+7 using matrix exponentiation.

Input

A single integer n.

Output

Print the n-th Fibonacci number modulo 10^9+7.

Examples


Input:
10

Output:
55

Solution in C++


#include <iostream>
#include <vector>
using namespace std;

const long long MOD = 1000000007;

struct Matrix {
    long long m[2][2];
};

Matrix mul(const Matrix &A, const Matrix &B){
    Matrix C = {{{0,0},{0,0}}};
    for(int i=0;i<2;i++){
        for(int j=0;j<2;j++){
            for(int k=0;k<2;k++){
                C.m[i][j] = (C.m[i][j] + A.m[i][k]*B.m[k][j]) % MOD;
            }
        }
    }
    return C;
}

Matrix power(Matrix A, long long n){
    Matrix result = {{{1,0},{0,1}}};
    while(n){
        if(n & 1) result = mul(result, A);
        A = mul(A, A);
        n /= 2;
    }
    return result;
}

int main(){
    long long n; cin >> n;
    if(n == 0) { cout << 0; return 0; }
    Matrix F = {{{1,1},{1,0}}};
    F = power(F, n-1);
    cout << F.m[0][0];
    return 0;
}