You are given an integer array nums indexed starting at $0$, which represents a pile of elements where the element at index $0$ is at the top of the pile.

In a single move, you can perform either of the following operations:

• If the pile is not empty, remove the topmost element from the pile.

• If at least $1$ element has been removed, select any previously removed element and place it back onto the top of the pile.

You are also given an integer k, representing the total number of moves you must perform.

Return the maximum possible value of the topmost element of the pile after executing exactly k moves. If it is impossible to have any elements remaining in the pile after k moves, return $-1$.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $0 \leq$ nums[i], k $\leq 10^9$

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.