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