#include <bits/stdc++.h>
using namespace std;
typedef long long LL;

 
// aのb乗をO(log b)で計算する
LL pow_mod(LL a, LL b, LL mod){
    if(b == 0) return 1;
    LL res = pow_mod(a * a % mod, b / 2, mod);
    if(b & 1) res = res * a % mod;
    return res;
}

int main(){
LL a, b;
cin >> a >> b;
cout << pow_mod(a, b, 1000000007) << endl;
}
### Prompt

Develop a solution in CPP to the problem described below:

For given integers m and n, compute mn (mod 1,000,000,007). Here, A (mod M) is the remainder when A is divided by M.

Constraints

* 1 ≤ m ≤ 100
* 1 ≤ n ≤ 109

Input


m n


Two integers m and n are given in a line.

Output

Print mn (mod 1,000,000,007) in a line.

Examples

Input

2 3


Output

8


Input

5 8


Output

390625

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;

 
// aのb乗をO(log b)で計算する
LL pow_mod(LL a, LL b, LL mod){
    if(b == 0) return 1;
    LL res = pow_mod(a * a % mod, b / 2, mod);
    if(b & 1) res = res * a % mod;
    return res;
}

int main(){
LL a, b;
cin >> a >> b;
cout << pow_mod(a, b, 1000000007) << endl;
}
```