2109: The Sum of the k-th Powers
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
[Submit] [Status] [Web Board] [Creator:]
Description
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