Fruits are placed on an infinite number line. You are given a $2$D integer array fruits where fruits[i] = [ position_i, amount_i ] indicates that there are amount_i fruits positioned at coordinate position_i. The array fruits is sorted by position_i in strictly ascending order.

You are also given two integers startPos and k. Initially, you are at position startPos. In one step, you can move $1$ unit to the left or $1$ unit to the right. You can walk at most k steps in total. Whenever you reach a coordinate containing fruits, you collect all fruits at that location. Each fruit can only be collected once.

Return the maximum total number of fruits you can collect.

Constraints:

• $1 \leq$ fruits.length $\leq 10^5$

• fruits[i].length $= 2$

• $0 \leq$ startPos, position_i $\leq 2 imes 10^5$

• position_$_{i-1} <$ position_$_i$ for any $i > 0$ ($0$ indexed)

• $1 \leq$ amount_i $\leq 10^4$

• $0 \leq$ k $\leq 2 imes 10^5$

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.

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