#include <bits/stdc++.h>
using namespace std;
int N, M;
const int mod = 1e9 + 7;
int f[1000001];
int main() {
  cin >> N >> M;
  f[N] = 1;
  int k = 0;
  for (int i = N - 1; i >= 0; --i) {
    f[i] = 1LL * M * ((2 * f[i + 1] - k) % mod + mod) % mod;
    k = (1LL * (M - 1) * k % mod + f[i + 1]);
  }
  cout << f[0] << endl;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

For a sequence a of n integers between 1 and m, inclusive, denote f(a) as the number of distinct subsequences of a (including the empty subsequence).

You are given two positive integers n and m. Let S be the set of all sequences of length n consisting of numbers from 1 to m. Compute the sum f(a) over all a in S modulo 109 + 7.

Input

The only line contains two integers n and m (1 ≤ n, m ≤ 106) — the number of elements in arrays and the upper bound for elements.

Output

Print the only integer c — the desired sum modulo 109 + 7.

Examples

Input

1 3


Output

6


Input

2 2


Output

14


Input

3 3


Output

174

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int N, M;
const int mod = 1e9 + 7;
int f[1000001];
int main() {
  cin >> N >> M;
  f[N] = 1;
  int k = 0;
  for (int i = N - 1; i >= 0; --i) {
    f[i] = 1LL * M * ((2 * f[i + 1] - k) % mod + mod) % mod;
    k = (1LL * (M - 1) * k % mod + f[i + 1]);
  }
  cout << f[0] << endl;
}

```