#include <bits/stdc++.h>

using namespace std;

int f(int n, int m) {
    if (m == 0) return 1;
    int res = f(n, m/2);
    res = (long long) res * res % 1000000007;
    if (m & 1) res = (long long) res * n % 1000000007;
    return res;
}

int main() {
    int n, m;
    cin >> n >> m;
    cout << f(n, m) << endl;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

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;

int f(int n, int m) {
    if (m == 0) return 1;
    int res = f(n, m/2);
    res = (long long) res * res % 1000000007;
    if (m & 1) res = (long long) res * n % 1000000007;
    return res;
}

int main() {
    int n, m;
    cin >> n >> m;
    cout << f(n, m) << endl;
}

```