Missing Numbers ~ Multiplex Coder

Alice (uniformly and independently) randomly picks two integers

a, b

from the range

[1, 10^{4}]

, and writes down the values of

a + b

a - b

a \cdot b

and

⌊ \frac{a}{b} ⌋

(integer division) in some random order. Unfortunately, she forgot the values of

a

and

b

. You need to help her to find out if there exists two integers

a, b

such that

1 \leq a, b \leq 10^{4}

and

a + b

a - b

a \cdot b

⌊ \frac{a}{b} ⌋

are the numbers she has written down.

If a solution exists, it is guaranteed to be unique.

Input Format

The first line of input contains a single integer $T$

, denoting the number of testcases. The description of

T

testcases follows.

Each testcase consists of a single line of input, containing four space-separated integers

A, B, C, D

— the values written down by Alice. It is guaranteed that at most one of the four numbers

A, B, C, D

will be negative.

Output Format

For each testcase, output in a single line, separated by a space, the two numbers Alice has chosen in order (i.e, if the solution is $a = 1$

and

b = 2

, print

1 2

and not

2 1

). If there does not exist any such choice of integers, print

- 1

twice, separated by a space, instead.

Constraints

$1 \leq T \leq 10^{5}$

- 10^{9} \leq A, B, C, D \leq 10^{9}

At most one of

A, B, C, D

is negative.

Subtasks

Subtask #1 (100 points): Original constraints

Sample Input 1

2
-1 72 0 17
1 4 5 6

Sample Output 1

8 9
-1 -1

Explanation

Test case $1$

: With

a = 8, b = 9

we obtain

8 + 9 = 17, 8 - 9 = - 1, 8 \cdot 9 = 72, ⌊ \frac{8}{9} ⌋ = 0

which are exactly the

4

numbers written down by Alice.

Test case $2$

: It can be shown that no choice of integers

a, b

can produce the given

4

numbers.

Missing Numbers