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 PYTHON3):

Solution:
n,k = map(int,input().split())
dp = [0 for i in range(k+1)]
mod = 10**9+7
dp[0] = 1
for i in range(k):
  for j in range(1,k+1)[::-1]:
    dp[j] = (dp[j]*j+dp[j-1]*(n-j+1))%mod
  dp[0] = 0
ans = 0
for i in range(k+1):
  if n < i:
    continue
  ans += dp[i]*pow(2,n-i,mod)
  ans %= mod

print(ans)