#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e6 + 100;
const int M = 1e9 + 7.1;
int f[maxn], s, n, m;
int mult(int a, int b) {
  long long c;
  c = (long long)a * (long long)b % M;
  return c;
}
int add(int a, int b) {
  int c = a + b;
  if (c >= M) {
    c -= M;
  }
  return c;
}
int sub(int a, int b) {
  if (a < b) {
    a += M;
  }
  return a - b;
}
void solve() {
  f[0] = 1;
  f[1] = 2 * m;
  int tmp = 0;
  for (int i = 2; i <= n; i++) {
    tmp = add(f[i - 2], mult(m - 1, tmp));
    f[i] = mult(m, add(f[i - 1], sub(f[i - 1], tmp)));
  }
  printf("%d\n", f[n]);
}
int main() {
  while (scanf("%d%d", &n, &m) != EOF) {
    solve();
  }
  return 0;
}

### Prompt

In cpp, your task is to solve 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 int maxn = 1e6 + 100;
const int M = 1e9 + 7.1;
int f[maxn], s, n, m;
int mult(int a, int b) {
  long long c;
  c = (long long)a * (long long)b % M;
  return c;
}
int add(int a, int b) {
  int c = a + b;
  if (c >= M) {
    c -= M;
  }
  return c;
}
int sub(int a, int b) {
  if (a < b) {
    a += M;
  }
  return a - b;
}
void solve() {
  f[0] = 1;
  f[1] = 2 * m;
  int tmp = 0;
  for (int i = 2; i <= n; i++) {
    tmp = add(f[i - 2], mult(m - 1, tmp));
    f[i] = mult(m, add(f[i - 1], sub(f[i - 1], tmp)));
  }
  printf("%d\n", f[n]);
}
int main() {
  while (scanf("%d%d", &n, &m) != EOF) {
    solve();
  }
  return 0;
}

```