Given an array arr that represents a permutation of integers from $1$ to n, you have a binary string of length n initially containing all $0$s.

At each step i (from $1$ to n), the bit at position arr[i - 1] ($1$ based index) is changed to $1$.

A group of $1$s is defined as a contiguous sequence of $1$s such that it cannot be extended to the left or to the right.

Return the latest step at which there exists a group of $1$s of length exactly m. If no such group exists at any step, return $-1$.

Constraints:

• n $==$ arr.length

• $1 \leq$ m $\leq$ n $\leq 10^5$

• $1 \leq$ arr[i] $\leq$ n

• All integers in arr are distinct.

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.