Problem Statement

On an infinitely long number line, there are Alice's house and shops. Alice's house is at coordinate $X$ on the number line. In addition, there is $1$ shop at every non-negative integer coordinate.

Alice is going to hold a birthday party at her house, so she has decided to buy decorations.

There are $N$ types of decorations, and the conditions on the shops where each decoration can be purchased are as follows.

• The $i$-th decoration can be purchased at the shop at coordinate $x$ if and only if $x \& 2^{c_i} \neq 0$.

Here, $a \& b$ denotes the bitwise AND of non-negative integers $a$ and $b$.

Alice can perform the following actions any number of times, $0$ or more, in any order.

• Move: Choose any integer $y$. Letting $x$ be Alice's current coordinate, change Alice's coordinate to $x + y$.
• Purchase: This can be performed only when Alice's current coordinate is a non-negative integer. Choose $1$ item that can be purchased at the shop at the current coordinate, and purchase it.

Here, the travel distance is defined as the sum of the absolute values of the chosen values over all Moves.

Initially, Alice is at her house. Find the minimum possible travel distance for Alice, by repeating actions, to purchase $1$ decoration of every type and return to her house.

You are given $T$ test cases; answer each of them.

Constraints

• All input values are integers.
• $1 \leq T \leq 1000$
• $1 \leq N \leq 60$
• $0 \leq c_1 < c_2 < \dots < c_N < 60$
• $0 \leq X < 2^{60}$

Input

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

$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$

Each test case is given in the following format.

$N$ $X$
$c_1$ $c_2$ $\dots$ $c_N$

Output

Print $T$ lines. On the $i(1 \leq i \leq T)$-th line, print the answer to the $i$-th test case.

Sample

4
2 10
0 2
1 0
3
4 15
0 1 2 3
5 20240822
0 5 7 8 18

4
16
0
2