There are n uniquely$-$sized planks whose lengths are integers from $1$ to n$.$ You need to arrange the planks such that exactly k planks are visible from the top. A plank is visible from the top if there are no longer planks to the top of it$.$

For example, if the planks are arranged $[1,3,2,5,4],$ then the planks with lengths $1,3,$ and $5$ are visible from the top.

Given n and k$,$ return the number of such arrangements. Since the answer may be large, return it modulo $109+7.$

Constraints:

$1<=$n$<=1000$

$1<=$k$<=$n

Test case $0$:

Input: n$=3,$ k$=2$

Output: $3$

Test case $1$:

Input: n$=5,$ k$=5$

Output: $1$