You are given an integer array happiness of length n and a positive integer k.

There are n children standing in a line, where the happiness value of the $i^{ ext{th}}$ child is given by happiness[i]. You want to select k children in k turns, choosing exactly $1$ child in each turn.

In each turn, once you pick a child, the happiness value of all the remaining unselected children decreases by $1$. A child’s happiness value cannot decrease below $0$.

Return the maximum possible sum of the happiness values of the $k$ children you can select.

Constraints:

• $1 \leq n ==$ happiness.length $\leq 2 imes 10^5$

• $1 \leq$ happiness[i] $\leq 10^8$

• $1 \leq k \leq n$

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.