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 $\leq 10^6$

The key insight is that since x$^i$ and y$^j$ grow exponentially, the number of distinct powers of x and y that remain within bound is at most $O(\log(\text{bound}))$ each. We can enumerate all pairs $(i, j)$ by iterating through powers of x in an outer loop and powers of y in an inner loop, adding each sum x$^i$ ...