#P622F. The Sum of the k-th Powers
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ID: 7055
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: 10
Uploaded By:
Hydro
Tags> The Sum of the k-th Powers
Description
There 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).
The only line contains two integers n, k (1 ≤ n ≤ 109, 0 ≤ k ≤ 106).
Print the only integer a — the remainder after dividing the value of the sum 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.
4 1
4 2
4 3
4 0
10
30
100
4