CF1542B Plus and Multiply

There is an infinite set generated as follows: - $ 1 $ is in this set. - If $ x $ is in this set, $ x \cdot a $ and $ x+b $ both are in this set. For example, when $ a=3 $ and $ b=6 $ , the five smallest elements of the set are: - $ 1 $ , - $ 3 $ ( $ 1 $ is in this set, so $ 1\cdot a=3 $ is in this set), - $ 7 $ ( $ 1 $ is in this set, so $ 1+b=7 $ is in this set), - $ 9 $ ( $ 3 $ is in this set, so $ 3\cdot a=9 $ is in this set), - $ 13 $ ( $ 7 $ is in this set, so $ 7+b=13 $ is in this set). Given positive integers $ a $ , $ b $ , $ n $ , determine if $ n $ is in this set.

N/A

N/A

In the first test case, $ 24 $ is generated as follows: - $ 1 $ is in this set, so $ 3 $ and $ 6 $ are in this set; - $ 3 $ is in this set, so $ 9 $ and $ 8 $ are in this set; - $ 8 $ is in this set, so $ 24 $ and $ 13 $ are in this set. Thus we can see $ 24 $ is in this set. The five smallest elements of the set in the second test case is described in statements. We can see that $ 10 $ isn't among them.