Statement

To celebrate his recovery, k1o0n has baked an enormous $n$ metres long potato casserole.

Turns out, Noobish_Monk just can't stand potatoes, so he decided to ruin k1o0n's meal. He has cut it into $k$ pieces, of lengths $a_1, a_2, \dots, a_k$ meters.

k1o0n wasn't keen on that. Luckily, everything can be fixed. In order to do that, k1o0n can do one of the following operations:

• Pick a piece with length $a_i \ge 2$ and divide it into two pieces with lengths $1$ and $a_i - 1$ . As a result, the number of pieces will increase by $1$ ;
• Pick a slice $a_i$ and another slice with length $a_j=1$ ( $i \ne j$ ) and merge them into one piece with length $a_i+1$ . As a result, the number of pieces will decrease by $1$ .

Help k1o0n to find the minimum number of operations he needs to do in order to merge the casserole into one piece with length $n$ .

For example, if $n=5$ , $k=2$ and $a = [3, 2]$ , it is optimal to do the following:

1. Divide the piece with length $2$ into two pieces with lengths $2-1=1$ and $1$ , as a result $a = [3, 1, 1]$ .
2. Merge the piece with length $3$ and the piece with length $1$ , as a result $a = [4, 1]$ .
3. Merge the piece with length $4$ and the piece with length $1$ , as a result $a = [5]$ .

Format

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 10^4$ ).

Description of each test case consists of two lines. The first line contains two integers $n$ and $k$ ( $2 \le n \le 10^9$ , $2 \le k \le 10^5$ ) — length of casserole and the number of pieces.

The second line contains $k$ integers $a_1, a_2, \ldots, a_k$ ( $1 \le a_i \le n - 1$ , $\sum a_i = n$ ) — lengths of pieces of casserole, which Noobish_Monk has cut.

It is guaranteed that the sum of $k$ over all $t$ test cases doesn't exceed $2 \cdot 10^5$ .

Output

For each test case, output the minimum number of operations K1o0n needs to restore his pie after the terror of Noobish_Monk.

Sample

4
5 3
3 1 1
5 2
3 2
11 4
2 3 1 5
16 6
1 6 1 1 1 6

2
3
9
15