970. Powerful Integers ¶

Problem

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

An integer is powerful if it can be represented as xⁱ + y^j for some integers i >= 0 and j >= 0.

You may return the answer in any order. In your answer, each value should occur at most once.

Example 1:

Input: x = 2, y = 3, bound = 10
Output: [2,3,4,5,7,9,10]
Explanation:
2 = 2⁰ + 3⁰
3 = 2¹ + 3⁰
4 = 2⁰ + 3¹
5 = 2¹ + 3¹
7 = 2² + 3¹
9 = 2³ + 3⁰
10 = 2⁰ + 3²

Example 2:

Input: x = 3, y = 5, bound = 15
Output: [2,4,6,8,10,14]

Constraints:

1 <= x, y <= 100
0 <= bound <= 10⁶