Team Work

Description:

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.

Sample Input:

1 1

Sample Output:

1

Sample Input:

3 2

Sample 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.