CF932E.Team Work

普及/提高-

通过率：0%

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题目描述

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.

输入格式

Only line of input contains two integers $N$ $(1<=N<=10^{9})$ representing total number of people and $k$ $(1<=k<=5000)$ .

输出格式

Output the sum of costs for all non empty subsets modulo $10^{9}+7$ .

输入输出样例

输入#1
```
1 1
```
输出#1
```
1
```
输入#2
```
3 2
```
输出#2
```
24
```

说明/提示

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 $1+1+4+1+4+4+9=24$ .

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