You are given two positive integers startPos and endPos. Initially, you are positioned at startPos on an infinite number line. In each step, you can move either $1$ unit to the left or $1$ unit to the right.

Return the total number of distinct ways to reach position endPos after moving exactly k steps. Since the answer may be large, return it modulo $10^9 + 7$.

Note: Two ways are considered different if the sequence of chosen directions at each step is not identical.

Constraints:

• $1 \leq$ startPos, endPos, 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.