You are given n dice, where each die has k faces numbered from $1$ to k.

Return the total number of possible ways to roll the dice such that the sum of the face-up values equals target. Since the answer can be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ n, k $\leq 30$

• $1 \leq$ target $\leq 1000$

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.