Alice and Bob are competing in an archery competition. The target consists of $12$ scoring sections numbered from $0$ to $11$. Each participant is given numArrows arrows to shoot.

Alice has already shot all of her arrows. You are given an integer numArrows and an integer array aliceArrows of length $12$, where aliceArrows[i] denotes the number of arrows Alice shot into the scoring section $i$.

Bob now wants to shoot his numArrows arrows to maximize his total points based on the following rules:

• For each scoring section $k$ from $0$ to $11$, if Bob shoots strictly more arrows than Alice into section $k$ (i.e., bobArrows[k] $>$ aliceArrows[k]), Bob is awarded $k$ points.

• Otherwise, Bob earns $0$ points for that section.

Return an integer array bobArrows of size $12$ representing the number of arrows Bob should shoot into each scoring section to maximize his total points. The sum of all values in bobArrows must be equal to numArrows. If there are multiple valid configurations that yield the maximum score, return any one of them.

Constraints:

• $1 \leq$ numArrows $\leq 10^5$

• aliceArrows.length $==$ bobArrows.length $== 12$

• $0 \leq$ aliceArrows[i], bobArrows[i] $\leq$ numArrows

• $\sum$ aliceArrows[i] $==$ numArrows

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.