The Sum of the k-th Powers
题目描述
F. The Sum of the k-th Powers
time limit per test
2 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputThere are well-known formulas: 
, 
, 
. Also mathematicians found similar formulas for higher degrees.
Find the value of the sum 
modulo 109+7 (so you should find the remainder after dividing the answer by the value 109+7).
Input
The only line contains two integers n,k (1≤n≤109,0≤k≤106).
Output
Print the only integer a − the remainder after dividing the value of the sum by the value 109+7.
Examples
Input
4 1
Output
10
Input
4 2
Output
30
Input
4 3
Output
100
Input
4 0
Output
4
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