Missing Numbers Problem Code: MISS_NUM | CodeChef Solution | Python3
Alice (uniformly and independently) randomly picks two integers a,b from the range [1,104], and writes down the values of a+b, a−b, a⋅b and ⌊ab⌋ (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≤a,b≤104 and a+b, a−b, a⋅b, ⌊ab⌋ 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≤T≤105
−109≤A,B,C,D≤109
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⋅9=72,⌊89⌋=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.
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