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())
m = 0x3b9aca07
v = 500000004
r = 0
p = pow(2, n, m)
a = [1] + [0] * k
for i in range(k):
    for j in range(i, -1, -1):
        a[j + 1] += a[j]
        a[j] = a[j] * j % m
for i in range(k + 1):
    r = (r + p * a[i]) % m
    p = p * v * (n - i) % m
print(r)