Project Euler #207: Integer partition equations

_{This problem is a programming version of Problem 207 from projecteuler.net}

For some positive integers , there exists an integer partition of the form ,
where , and are all positive integers and is a real number.

The first two such partitions are and .

Partitions where is also an integer are called .
For any let be the proportion of such partitions that are perfect with .
Thus .

In the following table are listed some values of

...

Find the smallest for which .

Input Format

First line of each test file contains a single integer that is the number of queries per test file. lines follow, with two integers and separated by a single space on each.

Constraints

Output Format

Print exactly lines with an answer for the corresponding query on each.

Sample Input 0

2
2 3
9 20

Sample Output 0

6
30

Explanation 0

, but , therefore, an answer for the first query is .
, which is the first value less than among all where .