You are given three integers n, m, and k.

An array arr of length n is called valid if:

• Each element arr[i] is an integer satisfying $1 \le$ arr[i] $\le$ m for all $0 \le$ i $< n$.

• There are exactly k indices i ($0 \le$ i $< n - 1$) such that both arr[i] and arr[i + 1] are even.

Return the total number of such valid arrays. Since the answer may be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \le$ n $\le 750$

• $0 \le$ k $\le$ n $- 1$

• $1 \le$ m $\le 1000$

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.