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

給定兩個非負整數 x 和 y，如果某一整數等於 x^i + y^j，其中整數 i >= 0 且 j >= 0，那麼我們認為該整數是一個強整數。

返回值小於或等於 bound 的所有強整數組成的列表。

你可以按任何順序返回答案。在你的回答中，每個值最多出現一次。

示例 1：

輸入：x = 2, y = 3, bound = 10
輸出：[2,3,4,5,7,9,10]
解釋： 
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

示例 2：

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

提示：

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

 8ms

 1 class Solution {
 2     func powerfulIntegers(_ x: Int, _ y: Int, _ bound: Int) -> [Int] {
 3         var xs:[Int] = [1]
 4         var ys:[Int] = [1]
 5         
 6         if x > 1
 7         {
 8             var p:Int = x
 9             while(p <= bound)
10             {
11                 xs.append(p)
12                 p *= x
13             }
14         }
15         
16         if y > 1
17         {
18             var p:Int = y
19             while(p <= bound)
20             {
21                 ys.append(p)
22                 p *= y
23             }
24         }
25         
26         var s:Set<Int> = Set<Int>()
27         for xx in xs
28         {
29             for yy in ys
30             {
31                 if xx + yy <= bound
32                 {
33                     s.insert(xx + yy)
34                 }
35             }
36         }
37         return Array(s)
38     }
39 }