# ---
# title: 970. Powerful Integers
# id: problem970
# author: Tian Jun
# date: 2020-10-31
# difficulty: Easy
# categories: Hash Table, Math
# link: <https://leetcode.com/problems/powerful-integers/description/>
# hidden: true
# ---
# 
# Given two positive 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`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
