Problem Statement

There is an array $A_1, \\ldots, A_N$, and initially $A_i = i$ for all $i$. Define the following routine $\\mathrm{shuffle}(L, R)$:

• If $R = L + 1$, swap values of $A_L$ and $A_R$ and terminate.
• Otherwise, run $\\mathrm{shuffle}(L, R - 1)$ followed by $\\mathrm{shuffle}(L + 1, R)$.

Suppose we run $\\mathrm{shuffle}(1, N)$. Print the value of $A_K$ after the routine finishes.

For each input file, solve $T$ test cases.

Constraints

• $1 \\leq T \\leq 1000$
• $2 \\leq N \\leq 10^{18}$
• $1 \\leq K \\leq N$

Input

The input is given from Standard Input in the following format:

$T$ $case_1$ $case_2$ $\\vdots$ $case_T$

Each case is in the following format:

$N$ $K$

Output

Print $T$ lines. The $i$-th line should contain the answer for the $i$-th case.

Sample Input 1

7
2 1
2 2
5 1
5 2
5 3
5 4
5 5

Sample Output 1

2
1
2
4
1
5
3

For $N=2$, we do the following and get $A=(2,1)$.

• Run $\\mathrm{shuffle}(1, 2)$, and swap $A_1$ and $A_2$.

For $N=5$, we do the following and get $A=(2,4,1,5,3)$.

• Run $\\mathrm{shuffle}(1, 5)$:
  • Run $\\mathrm{shuffle}(1, 4)$:
    • Run $\\mathrm{shuffle}(1, 3)$:
      • $\\vdots$
    • Run $\\mathrm{shuffle}(2, 4)$:
      • $\\vdots$
  • Run $\\mathrm{shuffle}(2, 5)$:
    • Run $\\mathrm{shuffle}(2, 4)$:
      • $\\vdots$
    • Run $\\mathrm{shuffle}(3, 5)$:
      • $\\vdots$