1542B · Plus and Multiply

Problem: 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.

Input Format: The input consists of multiple test cases. The first line contains an integer $t$ ($1\leq t\leq 10^5$) — the number of test cases. The description of the test cases follows.

The only line describing each test case contains three integers $n$, $a$, $b$ ($1\leq n,a,b\leq 10^9$) separated by a single space.

Output Format: For each test case, print "Yes" if $n$ is in this set, and "No" otherwise. You can print each letter in any case.

Note: 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.