Divisors and Reciprocals solution codechef

Alice is teaching Bob maths via a game called $N$ -guesser.

Alice has a positive integer $N$ which Bob needs to guess. She gives him two pieces of information with which to do this:

A positive integer $X$ , which denotes the sum of divisors of $N$ .
Two positive integers $A$ and $B$ , which denote that the sum of reciprocals of divisors of $N$ is $A / B$ .

Bob either needs to guess $N$ or tell that no such number exists.

It can be shown that if a valid $N$ exists, it is unique.

The first line of input contains a single integer $T$ , denoting the number of test cases. The description of $T$ test cases follows.
Each test case consists of a single line of input, containing three space-separated integers $X, A, B$ .

For each test case, output a new line containing the answer — Alice’s number $N$ , or $- 1$ if no such number exists.

2
4 4 3
4 1 1

3
-1

Test case $1$ : The divisors of $3$ are $1$ and $3$ . Their sum is $4$ and the sum of their reciprocals is $4 / 3$ .

Test case $2$ : It can be proved that no positive integer $N$ exists whose divisors sum to $4$ and reciprocals of divisors sum to $1$ .

For Solution