Problem: You have a team of N people. For a particular task, you can pick any non-empty subset of people. The cost of having x people for the task is xk. 

Output the sum of costs over all non-empty subsets of people.

Input

Only line of input contains two integers N (1 ≤ N ≤ 109) representing total number of people and k (1 ≤ k ≤ 5000).

Output

Output the sum of costs for all non empty subsets modulo 109 + 7.

Examples

Input

1 1


Output

1


Input

3 2


Output

24

Note

In the first example, there is only one non-empty subset {1} with cost 11 = 1.

In the second example, there are seven non-empty subsets.

- {1} with cost 12 = 1

- {2} with cost 12 = 1

- {1, 2} with cost 22 = 4

- {3} with cost 12 = 1

- {1, 3} with cost 22 = 4

- {2, 3} with cost 22 = 4

- {1, 2, 3} with cost 32 = 9

The total cost is 1 + 1 + 4 + 1 + 4 + 4 + 9 = 24.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long P = 1000000007;
long long n, m;
long long f[2][5010], g[5010];
inline long long pm(long long x, long long y) {
  long long z = 1;
  while (y) {
    if (y & 1) z = z * x % P;
    x = x * x % P, y >>= 1;
  }
  return z;
}
int main() {
  scanf("%lld%lld", &n, &m);
  int i, j, d;
  if (n <= m) {
    for (i = 0; i <= n; i++) {
      d = i & 1;
      memset(f[d], 0, sizeof(f[d]));
      f[d][0] = 1;
      for (j = 1; j <= i; j++) f[d][j] = (f[d ^ 1][j - 1] + f[d ^ 1][j]) % P;
    }
    long long ans = 0;
    for (i = 1; i <= n; i++) ans = (ans + f[n & 1][i] * pm(i, m)) % P;
    printf("%lld", ans);
    return 0;
  }
  long long tmp = pm(2, n - m);
  for (i = 1; i <= m + 1; i++) g[i] = 1;
  for (i = m; i >= 0; i--) f[0][i] = tmp - 1, tmp = (tmp << 1) % P;
  for (i = 1; i <= m; i++) {
    d = i & 1;
    memset(f[d], 0, sizeof(f[d]));
    for (j = 0; j <= m - i; j++)
      f[d][j] =
          ((n - j) * (f[d ^ 1][j + 1] + g[j + 1]) % P + j * f[d ^ 1][j]) % P,
      g[j + 1] = g[j + 1] * (j + 1) % P;
  }
  printf("%lld", f[m & 1][0]);
  return 0;
}