A11630 | Team Work
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内存限制256MB
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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.
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
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 $1+1+4+1+4+4+9=24$ .
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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评测结果：Accepted