A. Number Transformation
constructive algorithms; math
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.
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 \(y\) (\(1 \le x, y \le 100\)).
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.