A15737. Exponential Equation
编程题
普及/提高-
知识点
题目描述
You are given an integer $n$ .
Find any pair of integers $(x,y)$ ( $1\leq x,y\leq n$ ) such that $x^y\cdot y+y^x\cdot x = n$ .
Find any pair of integers $(x,y)$ ( $1\leq x,y\leq n$ ) such that $x^y\cdot y+y^x\cdot x = n$ .
输入格式
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 $n$ ( $1\leq n\leq 10^9$ ).
Each test case contains one line with a single integer $n$ ( $1\leq n\leq 10^9$ ).
输出格式
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 $-1$ .
Otherwise, print $-1$ .
输入输出样例
输入 #1
5 3 7 42 31250 20732790
输出 #1
-1 -1 2 3 5 5 3 13
说明/提示
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.
In the fourth test case, $5^5 \cdot 5+5^5 \cdot 5 = 31250$ , so $(5,5)$ is a legal solution.