**Time limit:**1.00 s**Memory limit:**512 MB

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`