Exponential Equation

给你一个整数 $n$，要你找整数对 $(x,y)$，使得 $x^y\times y+y^x\times x=n$。 第一行给你一个整数 $t$，表示 $t$ 组数据。 接下来 $t$ 行，每行给你一个整数 $n$。 对于每组数据，如果有解，输出任意一对 $(x,y)$，如果无解，输出 $-1$。

You are given an integer $ n $ . Find any pair of integers $ (x,y) $ ( $ 1\leq x,y\leq n $ ) such that $ x^y\cdot y+y^x\cdot x = n $ .

The first line contains a single integer $ t $ ( $ 1\leq t\leq 10^4 $ ) — the number of test cases. Each test case contains one line with a single integer $ n $ ( $ 1\leq n\leq 10^9 $ ).

For each test case, if possible, print two integers $ x $ and $ y $ ( $ 1\leq x,y\leq n $ ). If there are multiple answers, print any. Otherwise, print $ -1 $ .

5
3
7
42
31250
20732790

-1
-1
2 3
5 5
3 13

In the third test case, $ 2^3 \cdot 3+3^2 \cdot 2 = 42 $ , so $ (2,3),(3,2) $ will be considered as legal solutions. In the fourth test case, $ 5^5 \cdot 5+5^5 \cdot 5 = 31250 $ , so $ (5,5) $ is a legal solution.