CF622F.The Sum of the k-th Powers

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题目描述

There are well-known formulas: , , . Also mathematicians found similar formulas for higher degrees.

Find the value of the sum modulo 109+710^{9}+7 (so you should find the remainder after dividing the answer by the value 109+710^{9}+7 ).

输入格式

The only line contains two integers n,kn,k ( 1<=n<=109,0<=k<=1061<=n<=10^{9},0<=k<=10^{6} ).

输出格式

Print the only integer aa — the remainder after dividing the value of the sum by the value 109+710^{9}+7 .

输入输出样例

  • 输入#1

    4 1
    

    输出#1

    10
    
  • 输入#2

    4 2
    

    输出#2

    30
    
  • 输入#3

    4 3
    

    输出#3

    100
    
  • 输入#4

    4 0
    

    输出#4

    4
    
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