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3696: The Sum of the k-th Powers

Memory Limit：256 MB Time Limit：2.000 S
Judge Style：Text Compare Creator：
Submit：0 Solved：0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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).

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