You are given two integers, n and k. There are n uniquely sized sticks with lengths ranging from $1$ to n. You need to arrange these sticks in a single line such that looking from the left, exactly k sticks are visible. A stick is visible from the left if there are no sticks to its left that have a greater length.

Return the total number of permutations of the sticks such that exactly k sticks are visible from the left. Since the answer can be large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ n $\leq 1000$

• $1 \leq$ k $\leq$ n

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.