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 + yj 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

class Solution {
    public List<Integer> powerfulIntegers(int x, int y, int bound) {
        Set<Integer> set = new HashSet();
        int a = 1;
        while(a < bound) {
            int b = 1;
            while(b < bound) {
                if(a + b <= bound) set.add(a + b);
                if(y == 1) break;
                b *= y;
            }
            if(x == 1) break;
            a *= x;
        }
        return new ArrayList(set);
    }
}

a = a*x，b = b*y。a、b都从1开始。

外循环是a<bound, 内循环是b < bound, 先算内循环的，如果a+b《= bound就添加到set中，但是如果y是1就break，否则剩下的全是11111，如果不是1就更新b。

外循环也一样，如果x是1就直接break，否则就更新a = a*x。

最后返回。