Given three integers x, y, and bound, return a list of all powerful integers whose value is less than or equal to bound.

An integer is considered powerful if it can be expressed as x$^i$ + y$^j$ for some non negative integers $i$ and $j$ (i.e., $i \geq 0$ and $j \geq 0$).

The result may be returned in any order, and each value should appear at most once in the output.

Constraints:

• $1 \leq$ x, y $\leq 100$

• $0 \leq$ bound $\leq 10^6$

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.