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 `x`

for some integers ^{i} + y^{j}`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 = 10Output:[2,3,4,5,7,9,10]Explanation:2 = 2^{0}+ 3^{0}3 = 2^{1}+ 3^{0}4 = 2^{0}+ 3^{1}5 = 2^{1}+ 3^{1}7 = 2^{2}+ 3^{1}9 = 2^{3}+ 3^{0}10 = 2^{0}+ 3^{2}

**Example 2:**

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

**Constraints:**

`1 <= x, y <= 100`

`0 <= bound <= 10`

^{6}

class Solution {
public List<Integer> powerfulIntegers(int x, int y, int bound) {
}
}