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:

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

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.

Angry Monk

Examples