You are given two $1$ indexed integer arrays, nums of length $n$ and changeIndices of length $m$.

Initially, all indices from $1$ to $n$ are unmarked. In each second, starting from second $1$ up to second $m$, you can perform exactly one of the following actions:

• Choose an index $i$ such that $1 \leq i \leq n$ and decrease nums[i] by $1$.

• Mark index changeIndices[s] if nums[changeIndices[s]] equals $0$.

• Do nothing.

Return the earliest second at which all indices from $1$ to $n$ can be marked. If it is impossible to mark all indices within $m$ seconds, return $-1$.

Constraints:

• $1 \leq n ==$ nums.length $\leq 2000$

• $0 \leq$ nums[i] $\leq 10^9$

• $1 \leq m ==$ changeIndices.length $\leq 2000$

• $1 \leq$ changeIndices[i] $\leq n$

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.