Short Task

题意翻译

设$d(n)$为$n$的约数和。 给定$n$，求满足$d(i)=n$最小的$i$。 $t$组数据，每个答案一行

题目描述

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 $ .

输入输出格式

输入格式

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 $ ).

输出格式

For each test case, output: - "-1" if there is no such $ n $ that $ d(n) = c $ ; - $ n $ , otherwise.

输入输出样例

输入样例 #1

12
1
2
3
4
5
6
7
8
9
10
39
691

输出样例 #1

1
-1
2
3
-1
5
4
7
-1
-1
18
-1