You are given an integer array numWays, where numWays[i - 1] represents the number of distinct combinations to form an amount of $i$ (for $1 \leq i \leq$ numWays.length) using an infinite supply of coins with distinct positive integer denominations.

Return an array containing the coin denominations in strictly increasing order that produces the given numWays array. If no such set of denominations exists, return an empty array.

Constraints:

• $1 \leq$ numWays.length $\leq 100$

• $0 \leq$ numWays[i] $\leq 2 imes 10^8$

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.