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>
inline int calc(int x, int y) {
  int z = 1;
  for (; y; x = (long long)x * x % 1000000007, y >>= 1)
    if (y & 1) z = (long long)x * z % 1000000007;
  return z;
}
int a[5005], i, j, m, n, x, y;
int main() {
  scanf("%d%d", &n, &m);
  for (*a = i = 1; i <= m; *a = 0, i++)
    for (j = i; j; j--) a[j] = (a[j - 1] + (long long)a[j] * j) % 1000000007;
  for (i = 0, x = calc(2, n); i <= m;
       x = 500000004ll * x % 1000000007 * (n - i++) % 1000000007)
    y = (y + (long long)x * a[i]) % 1000000007;
  return 0 & printf("%d\n", y);
}