7651: [CSES Problem Set] Josephus Queries
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Description
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?"
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.
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
$1≤q≤10^5$
$1 \le k \le n \le 10^9$
$1 \le k \le n \le 10^9$
Sample 1 Input
4
7 1
7 3
2 2
1337 1313
Sample 1 Output
2
6
1
1107