G. Short Task
brute force; dp; math; number theory
Let us denote by \(d(n)\) the sum of all divisors of the number \(n\), i.e. \(d(n) = \sum\limits_{k | n} k\).For example, \(d(1) = 1\), \(d(4) = 1+2+4=7\), \(d(6) = 1+2+3+6=12\).For a given number \(c\), find the minimum \(n\) such that \(d(n) = c\).
The first line contains one integer \(t\) (\(1 \le t \le 10^4\)). Then \(t\) test cases follow.Each test case is characterized by one integer \(c\) (\(1 \le c \le 10^7\)).
For each test case, output: ""-1"" if there is no such \(n\) that \(d(n) = c\); \(n\), otherwise.