#include <bits/stdc++.h>
using namespace std;
const long long md = 1e9 + 7;
int main() {
  cin.sync_with_stdio(false);
  long long n, m;
  cin >> n >> m;
  vector<long long> s(n + 1);
  long long sub = 0;
  s[0] = 1;
  for (int i = (1); i < int(n + 1); ++i) {
    sub = sub * (m - 1);
    if (i >= 2) sub += s[i - 2];
    sub %= md;
    s[i] = (2 * m * s[i - 1] - m * sub) % md;
  }
  cout << (s[n] + md) % md << endl;
}

### Prompt

Please formulate a Cpp solution to the following problem:

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;
const long long md = 1e9 + 7;
int main() {
  cin.sync_with_stdio(false);
  long long n, m;
  cin >> n >> m;
  vector<long long> s(n + 1);
  long long sub = 0;
  s[0] = 1;
  for (int i = (1); i < int(n + 1); ++i) {
    sub = sub * (m - 1);
    if (i >= 2) sub += s[i - 2];
    sub %= md;
    s[i] = (2 * m * s[i - 1] - m * sub) % md;
  }
  cout << (s[n] + md) % md << endl;
}

```