You have N boxes numbered 1 through N and K candies numbered 1 through K. You put the candies in the boxes in the following order:

• first candy in the first box,
• second candy in the second box,
• ....... 
• ........
• so up to N-th candy in the Nth box,
• the next candy in (N - 1)-th box,
• the next candy in (N - 2)-th box
• ........
• .......
• and so on up to the first box, 
• then the next candy in the second box 
•  ......    and so on until there is no candy left.

So you put the candies in the boxes in the following order: \(1, 2, 3, ...., N, N - 1, N - 2, ...., 2, 1, 2, 3, ...., N, N - 1, ....\)

Find the index of the box where you put the K-th candy.

Input format

• The first line contains T denoting the number of test cases. The description of T test cases is as follows:
• Each test case consists of a single line containing two integers N, and K.

Output format

For each test case, print the index of the box where you put the K-th candy.

Constraints

\(1 \leq T \leq 10^5 \\ 2 \leq N\leq 10^9\\ 1 \leq K\leq 10^9\)