Educational Codeforces Round 7 |
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Finished |

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F. The Sum of the k-th Powers

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 10^{9} + 7 (so you should find the remainder after dividing the answer by the value 10^{9} + 7).

Input

The only line contains two integers *n*, *k* (1 ≤ *n* ≤ 10^{9}, 0 ≤ *k* ≤ 10^{6}).

Output

Print the only integer *a* — the remainder after dividing the value of the sum by the value 10^{9} + 7.

Examples

Input

4 1

Output

10

Input

4 2

Output

30

Input

4 3

Output

100

Input

4 0

Output

4

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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