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

$1 \le t \le 100$

$1\le X,Y \le10^9$