#D10882. th Powers
th Powers
th Powers
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
inputFormat
Input
The only line contains two integers n, k (1 ≤ n ≤ 109, 0 ≤ k ≤ 106).
outputFormat
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
样例
4 1
10