Given two non-negative integers x and y, an integer is powerful if it is equal to x^i + y^j for some integers i >= 0 and j >= 0.

Return a list of all powerful integers that have value less than or equal to bound.

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 = 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 = 15
Output: [2,4,6,8,10,14]
 

Note:

1 <= x <= 100
1 <= y <= 100
0 <= bound <= 10^6
 

class Solution {
    public List<Integer> powerfulIntegers(int x, int y, int bound) {
        List<Integer> res = new ArrayList<>();
        // 用set是因為會有重複的情況
        Set<Integer> set = new HashSet<>();
        for(int a = 1; a <= bound; a *= x) {
            for(int b = 1; a + b <= bound; b *= y) {
                set.add(a+b);
                if(y == 1) break;
            }
            if(x == 1) break;
        }
        res.addAll(set);
        return res;
    }
}