# The Sum of the k-th Powers

Time Limit: 2 seconds

Memory Limit: 256 megabytes

## 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).

## 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.

## Sample Input

Input4 1Output10Input4 2Output30Input4 3Output100Input4 0Output4

## Sample Output

None

None

None