Your task is to count the number of sequences of length $n$ where each element is an integer between $1 \dots k$ and each integer between $1 \dots k$ appears at least once in the sequence.

For example, when $n=6$ and $k=4$, some valid sequences are $[1,3,1,4,3,2]$ and $[2,2,1,3,4,2]$.

Input

The only input line has two integers $n$ and $k$.

Output

Print one integer: the number of sequences modulo $10^9+7$.

Constraints

• $1 \le k \le n \le 10^6$

Example

Input:

6 4

Output:

1560