You are given two integers \(X\) and \(Y\). Your task is to determine the sequence of real numbers with the minimum size such that the sum and product of the numbers in the sequence are \(X\) and \(Y\) respectively. Also, print the size of the sequence only.

If no such sequences exist, then print \(-1\).

Input format

• First line: \(t\) denoting the number of test cases
• Next \(t\) lines: Two space-separated integers \(X\) and \(Y\)

Output format

For each test case, print a single line containing the answer.

Constraints

\(1 \le t \le 100\)

\(1\le X,Y \le10^9\)