시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
3 초 (추가 시간 없음) 512 MB 4 3 3 75.000%

## 문제

Integer factorization serves an important role in many cryptography systems. It is about finding two positive integers p and q for a given positive composite number n such that n = pq and 1 < p ≤ q < n. However, it is a well-known NP-intermediate candidate. We still don’t have any algorithm to solve it in polynomial time.

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

Given a prime number p and two integers a0, a1 ∈ {0, 1, . . . p − 1}. Find two integers b0, b1 ∈ {0, 1, . . . p − 1} such that a0 ≡ b0 · b1 (mod p) and a1 ≡ b0 + b1 (mod p).

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

## 입력

The first line contains an integer 1 ≤ T ≤ 100 indicating the number of test cases. For each test case, there is a line containing three non-negative integers p, a0, a1 separated by a single blank.

## 출력

For each test case, output a line containing b0 and b1 in ascending order separated by a single blank if b0 and b1 satisfy the equations. If there are multiple solutions, you may output any of them. If there is no solution, output −1.

## 제한

• 1 ≤ T ≤ 100
• 1 < p < 231 and p is a prime number.
• a0, a1 ∈ {0, 1, . . . , p − 1}.

## 예제 입력 1

2
2 1 0
2 1 1


## 예제 출력 1

1 1
-1