INS16H - Daenerys wants to Conquer

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With full zeal, Daenerys Targaryen is looking to conquer the seven kingdoms. In need of wise commanders, she wants them to solve the below problem:

Given the following function F and an integer N find the smallest integer x satisfying F(x) = N.

If no such x exists, print “-1”. (without quotes)

Input Format:

The first line contains one integer T, the number of times she gives you the problem.

T lines follow, each containing a single integer N.

Output Format:

Print the answer for each problem in a separate line.

Constraints:

1 ≤ T ≤ 10

1 ≤ N ≤ 1010

Sample Input:

4

5

4

9

7

Sample Output:

4

3

8

-1


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[Trichromatic] XilinX: 2018-05-22 07:39:56

F(x) can be find by the following PS-eudo code:
function f(x){
ret = 0
for d = 1..x:
if (x mod d == 0) and (gcd(d, x/d) == 1):
ret += d
return ret;
}

hodobox: 2018-05-22 05:00:32

The image with the actual function is missing - completely unsolvable without it.
Edit: I managed to find it
http://www.image-maps.com/m/private/0/gh741aeuifi28iqd8u2995i5a0_pv4ua.jpg


Added by:Adarsh kumar
Date:2016-04-10
Time limit:0.200s-1.200s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU JS-MONKEY
Resource:INSOMNIA 2016