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
inputCopy
1 1
outputCopy
1
inputCopy
3 2
outputCopy
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.
数学式子很容易推导出来，关键是怎么求；
标程的解法很独特：
看这位大佬的博客，有详细解释