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 int modd = 1e9 + 7;
const int MAXN = 5e3 + 10;
long long dp[MAXN][MAXN];
long long quick(long long a, long long n) {
  long long ans = 1;
  while (n) {
    if (n % 2) ans = ans * a % modd;
    a = a * a % modd;
    n /= 2;
  }
  return ans;
}
int main() {
  long long n, k;
  cin >> n >> k;
  dp[0][0] = 1;
  for (int i = 1; i <= k; i++) {
    for (int j = 1; j <= i; j++) {
      dp[i][j] =
          (n - j + 1) * dp[i - 1][j - 1] % modd + j * dp[i - 1][j] % modd;
      dp[i][j] %= modd;
    }
  }
  long long res = 0;
  long long tmp = quick(2, max(n - k, 0LL));
  for (int i = min(n, k); i >= 1; i--) {
    res += dp[k][i] * tmp % modd;
    res %= modd;
    tmp = tmp * 2 % modd;
  }
  cout << res << endl;
}