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;
template <class T>
void rd(T &ret) {
  ret = 0;
  bool ok = 0, u = 0;
  for (;;) {
    int c = getchar();
    if (c >= '0' && c <= '9')
      ret = (ret << 3) + (ret << 1) + c - '0', ok = 1;
    else if (c == '-')
      u = 1;
    else if (ok) {
      if (u) ret *= -1;
      return;
    }
  }
}
long long pow_mod(long long p, long long n, long long mod) {
  long long ret = 1;
  for (; n; n >>= 1) {
    if (n & 1) ret = ret * p % mod;
    p = p * p % mod;
  }
  return ret;
}
template <class T>
bool chmin(T &a, const T &b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool chmax(T &a, const T &b) {
  return b > a ? a = b, 1 : 0;
}
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
const long long mod = (int)1e9 + 7;
void add(int &a, int b) {
  a += b;
  if (a >= mod) a -= mod;
}
int dp[5555][5555];
int main() {
  int n, K;
  cin >> n >> K;
  dp[1][0] = 1;
  for (int i = (1); i < (K); i++)
    for (int j = (0); j < (i); j++) {
      if (j < n - 1) add(dp[i + 1][j + 1], dp[i][j]);
      add(dp[i + 1][j], (j + 1ll) * dp[i][j] % mod);
    }
  int ans = 0;
  long long t = 1;
  for (int i = (0); i < (K); i++) {
    t = t * (n - i) % mod;
    if (n - i - 1 >= 0)
      add(ans, (t * pow_mod(2, n - i - 1, mod) % mod) * dp[K][i] % mod);
  }
  cout << ans << endl;
  return 0;
}