#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
int p[1000010], fac[1000010], q[1000010], rev[1000010], n, m;
int modpow(int x, int n) {
  int rt = 1;
  while (n) {
    if (n & 1) rt = 1LL * rt * x % mod;
    x = 1LL * x * x % mod;
    n >>= 1;
  }
  return rt;
}
int C(int x, int y) { return (1LL * fac[x] * rev[y] % mod * rev[x - y] % mod); }
int main() {
  scanf("%d %d", &n, &m);
  p[0] = q[0] = fac[0] = rev[0] = 1;
  for (int i = 1; i <= n; i++) {
    p[i] = 1LL * m * p[i - 1] % mod;
    q[i] = 1LL * (m - 1) * q[i - 1] % mod;
    fac[i] = 1LL * i * fac[i - 1] % mod;
  }
  rev[n] = modpow(fac[n], mod - 2);
  for (int i = n - 1; i; i--) rev[i] = 1LL * rev[i + 1] * (i + 1) % mod;
  int ans = 0, cur = p[n];
  for (int i = 0; i <= n; i++) {
    ans = (ans + 1LL * cur * p[i]) % mod;
    int tp = 1LL * C(n, i) * q[n - i] % mod;
    cur = (cur - tp + mod) % mod;
  }
  cout << ans << endl;
}

### Prompt

Your task is to create 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 int mod = 1e9 + 7;
int p[1000010], fac[1000010], q[1000010], rev[1000010], n, m;
int modpow(int x, int n) {
  int rt = 1;
  while (n) {
    if (n & 1) rt = 1LL * rt * x % mod;
    x = 1LL * x * x % mod;
    n >>= 1;
  }
  return rt;
}
int C(int x, int y) { return (1LL * fac[x] * rev[y] % mod * rev[x - y] % mod); }
int main() {
  scanf("%d %d", &n, &m);
  p[0] = q[0] = fac[0] = rev[0] = 1;
  for (int i = 1; i <= n; i++) {
    p[i] = 1LL * m * p[i - 1] % mod;
    q[i] = 1LL * (m - 1) * q[i - 1] % mod;
    fac[i] = 1LL * i * fac[i - 1] % mod;
  }
  rev[n] = modpow(fac[n], mod - 2);
  for (int i = n - 1; i; i--) rev[i] = 1LL * rev[i + 1] * (i + 1) % mod;
  int ans = 0, cur = p[n];
  for (int i = 0; i <= n; i++) {
    ans = (ans + 1LL * cur * p[i]) % mod;
    int tp = 1LL * C(n, i) * q[n - i] % mod;
    cur = (cur - tp + mod) % mod;
  }
  cout << ans << endl;
}

```