Factorization

Integer factorization plays an important role in many cryptographic systems. It asks, for a given positive composite number $n$, to find two positive integers $p$ and $q$ such that $n = pq$ and $1 < p \le q < n$. It is a well-known NP-intermediate candidate, though, and no algorithm solves it in polynomial time yet.

Taylor, a number theorist, made another factorization problem as follows.

Given a prime number $p$ and two integers $a_0, a_1 \in \{0, 1, \ldots, p - 1\}$, find two integers $b_0, b_1 \in \{0, 1, \ldots, p - 1\}$ such that $a_0 \equiv b_0 \cdot b_1 \pmod{p}$ and $a_1 \equiv b_0 + b_1 \pmod{p}$.

"This factoring is way cooler, in that it can be computed efficiently," Taylor said. Now he invites you to enjoy this new variant of factorization.

The first line contains an integer $1 \le T \le 100$, the number of test cases. Each test case takes one line containing three non-negative integers $p, a_0, a_1$ separated by a single space.

For each test case, output one line containing $b_0$ and $b_1$ in ascending order separated by a single space if $b_0$ and $b_1$ satisfy the two equations. If there are multiple solutions, you may output any of them. If there is no solution, output $-1$.

• $1 \le T \le 100$
• $1 < p < 2^{31}$ and $p$ is prime.
• $a_0, a_1 \in \{0, 1, \ldots, p - 1\}$.