Number Transformation

题意翻译

$t$ 组数据，给出整数 $x,y$，找一组正整数 $a,b$ 使 $x\times b^a=y$，无解输出 `0 0`。 $1\le x,y\le100,t\le10^4$。

题目描述

You are given two integers $ x $ and $ y $ . You want to choose two strictly positive (greater than zero) integers $ a $ and $ b $ , and then apply the following operation to $ x $ exactly $ a $ times: replace $ x $ with $ b \cdot x $ . You want to find two positive integers $ a $ and $ b $ such that $ x $ becomes equal to $ y $ after this process. If there are multiple possible pairs, you can choose any of them. If there is no such pair, report it. For example: - if $ x = 3 $ and $ y = 75 $ , you may choose $ a = 2 $ and $ b = 5 $ , so that $ x $ becomes equal to $ 3 \cdot 5 \cdot 5 = 75 $ ; - if $ x = 100 $ and $ y = 100 $ , you may choose $ a = 3 $ and $ b = 1 $ , so that $ x $ becomes equal to $ 100 \cdot 1 \cdot 1 \cdot 1 = 100 $ ; - if $ x = 42 $ and $ y = 13 $ , there is no answer since you cannot decrease $ x $ with the given operations.

输入输出格式

输入格式

The first line contains one integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Each test case consists of one line containing two integers $ x $ and $ y $ ( $ 1 \le x, y \le 100 $ ).

输出格式

If it is possible to choose a pair of positive integers $ a $ and $ b $ so that $ x $ becomes $ y $ after the aforementioned process, print these two integers. The integers you print should be not less than $ 1 $ and not greater than $ 10^9 $ (it can be shown that if the answer exists, there is a pair of integers $ a $ and $ b $ meeting these constraints). If there are multiple such pairs, print any of them. If it is impossible to choose a pair of integers $ a $ and $ b $ so that $ x $ becomes $ y $ , print the integer $ 0 $ twice.

输入输出样例

输入样例 #1

3
3 75
100 100
42 13

输出样例 #1

2 5
3 1
0 0

题意翻译

$t$ 组数据，给出整数 $x,y$，找一组正整数 $a,b$ 使 $x\times b^a=y$，无解输出 `0 0`。 $1\le x,y\le100,t\le10^4$。