You are given two integers n and k.

Initially, an array a of length n is initialized where a[i] = $1$ for all $0 \leq i <$ n.

Every second, the array is updated such that each element at index i is replaced by the sum of all elements from index $0$ to index i from the previous second.

Return the value of the element at index n $- 1$ after k seconds.

Note: Since the answer can be large, return the result modulo $10^9 + 7$.

Constraints:

• $1 \leq$ n, k $\leq 1000$

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.