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 x^{k}. 

Output the sum of costs over all non-empty subsets of people.


-----Input-----

Only line of input contains two integers N (1 ≤ N ≤ 10^9) representing total number of people and k (1 ≤ k ≤ 5000).


-----Output-----

Output the sum of costs for all non empty subsets modulo 10^9 + 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 1^1 = 1.

In the second example, there are seven non-empty subsets.

- {1} with cost 1^2 = 1

- {2} with cost 1^2 = 1

- {1, 2} with cost 2^2 = 4

- {3} with cost 1^2 = 1

- {1, 3} with cost 2^2 = 4

- {2, 3} with cost 2^2 = 4

- {1, 2, 3} with cost 3^2 = 9

The total cost is 1 + 1 + 4 + 1 + 4 + 4 + 9 = 24.

Difficulty: VERY_HARD

Solutions:
MOD = 10 ** 9 + 7
INV = 500000004
(n, k) = map(int, input().split())
d = 1
p = pow(2, n, MOD)
ans = 0
stirling2_list = [0, 1]
for i in range(k - 1):
	stirling2_list = [0, 1] + [(stirling2_list[j - 1] + j * stirling2_list[j]) % MOD for j in range(2, 2 + i)] + [1]
for stirling in stirling2_list:
	ans = (ans + stirling * d * p) % MOD
	d = d * n % MOD
	n -= 1
	p = p * INV % MOD
print(ans)