CF1512G.Short Task

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.