You are given a string s representing a sequence of moves on a $2 ext{D}$ Cartesian plane and an integer k. A person starts at coordinate $(0, 0)$.

Each character in s represents a movement:

• 'U' moves $1$ unit up to $(x, y + 1)$

• 'D' moves $1$ unit down to $(x, y - 1)$

• 'L' moves $1$ unit left to $(x - 1, y)$

• 'R' moves $1$ unit right to $(x + 1, y)$

You must remove exactly one contiguous substring of length k from s. After the substring is removed, the remaining characters are concatenated in their original order, and the person executes the resulting sequence of moves starting from $(0, 0)$.

Return the number of distinct final coordinates reachable.

Constraints:

• $1 \leq$ s.length $\leq 10^5$

• s consists only of 'U', 'D', 'L', and 'R'

• $1 \leq$ k $\leq$ s.length

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.