Problem Statement

You are given a prime number $p$ and non-negative integers $a$ and $b$.

Determine if there is an infinite sequence of non-negative integers $t = \bigl(t(0), t(1), t(2), \ldots)$ that satisfies all of the following conditions.

• $0\leq t(x) < p$ for every non-negative integer $x$.
• $t(x+y)\bigl(1-t(x)t(y)\bigr)\equiv t(x)+t(y)\pmod{p}$ for all non-negative integers $x$ and $y$.
• $t(a)=b$.

You have $T$ test cases to solve.

Constraints

• $1\leq T\leq 2\times 10^5$
• $p$ is a prime number such that $1\leq p\leq 10^9$.
• $0\leq a\leq 10^{9}$
• $0\leq b < p$

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\vdots
\text{case}_T

Each test case is given in the following format:

p a b

Output

Print $T$ lines. The $i$-th line should contain Yes if there is a sequence of non-negative integers that satisfies all of the conditions, and No otherwise.