#include <bits/stdc++.h>
using namespace std;
const long long inf = (long long)1000000000000;
const double eps = (double)1e-8;
const int mod = (int)1000000007;
const int maxn = (int)1e5 + 5;
long long d[1000006], n, m;
void f(int x) {
  if (x <= 1 || d[x] != -1) return;
  f(x - 1);
  f(x - 2);
  d[x] = ((long long)(3 * m - 1) * d[x - 1] +
          ((m - (long long)2 * m * m) % mod) * d[x - 2]) %
         mod;
  return;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> m;
  memset(d, -1, sizeof d);
  d[0] = 1;
  d[1] = 2 * m;
  f(n);
  cout << d[n];
  return 0;
}

### Prompt

Develop a solution in CPP 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;
const long long inf = (long long)1000000000000;
const double eps = (double)1e-8;
const int mod = (int)1000000007;
const int maxn = (int)1e5 + 5;
long long d[1000006], n, m;
void f(int x) {
  if (x <= 1 || d[x] != -1) return;
  f(x - 1);
  f(x - 2);
  d[x] = ((long long)(3 * m - 1) * d[x - 1] +
          ((m - (long long)2 * m * m) % mod) * d[x - 2]) %
         mod;
  return;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> m;
  memset(d, -1, sizeof d);
  d[0] = 1;
  d[1] = 2 * m;
  f(n);
  cout << d[n];
  return 0;
}

```