Problem J
Juggling Sequence

The Juggling Sequence is an integer sequence with $n$ elements, defined as follow:

• $a_1=1$,

• For every $i\ge 1$:

  • If $a_i\le i$, then $a_{i+1}=a_i+i$,

  • If $a_i>i$, then $a_{i+1}=a_i-i$.

Let’s sort the juggling sequence in non-decreasing order. What is the $m$-th number?

Input

The first line of the input contains a single integer $t$ $(1\le t\le {10}^4)$ — the number of test cases.

$t$ test cases follow, each test case contains a single line with two integers $n$ and $m$ $(1\le m\le n\le {10}^{18})$.

Output

For each test case, print a single integer — the $m$-th number in the sorted juggling sequence.

Explanation of the sample input

With $n=6$, the juggling sequence is $1,2,4,1,5,10$. After sorting, the sequence becomes $1,1,2,4,5,10$.

3
6 1
6 2
6 6

1
1
10