Plus and Multiply
Description
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.
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.
For each test case, print "Yes" if $n$ is in this set, and "No" otherwise. You can print each letter in any case.
Input
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
For each test case, print "Yes" if $n$ is in this set, and "No" otherwise. You can print each letter in any case.
Samples
5
24 3 5
10 3 6
2345 1 4
19260817 394 485
19260817 233 264
Yes
No
Yes
No
Yes
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.