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

An array arr of size n is called good if:

• $1 \leq$ arr[i] $\leq$ m for every $0 \leq$ i $<$ n.

• There are exactly k indices i ($0 \leq$ i $<$ n $- 1$) such that arr[i] = arr[i + 1].

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

Constraints:

• $1 \leq$ n $\leq 10^5$

• $1 \leq$ m $\leq 10^5$

• $0 \leq$ k $\leq$ n $- 1$

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.