Consider a game where there are $n$ children (numbered $1,2,\dots,n$) in a circle. During the game, every second child is removed from the circle, until there are no children left.

Your task is to process $q$ queries of the form: "when there are $n$ children, who is the $k$th child that will be removed?"

Input

The first input line has an integer $q$: the number of queries.

After this, there are $q$ lines that describe the queries. Each line has two integers $n$ and $k$: the number of children and the position of the child.

Output

Print $q$ integers: the answer for each query.

Constraints

• $1 \le q \le 10^5$
• $1 \le k \le n \le 10^9$

Example

Input:

4
7 1
7 3
2 2
1337 1313

Output:

2
6
1
1107