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Powerful Integers

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.

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 <= 10^6

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