[Solution] Virus Codeforces Solution 2022

C. Virus

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

There are n$n$ houses numbered from 1$1$ to n$n$ on a circle. For each 1≤i≤n−1$1\le i\le n-1$, house i$i$ and house i+1$i+1$ are neighbours; additionally, house n$n$ and house 1$1$ are also neighbours.

Initially, m$m$ of these n$n$ houses are infected by a deadly virus. Each morning, Cirno can choose a house which is uninfected and protect the house from being infected permanently.

Every day, the following things happen in order:

• Cirno chooses an uninfected house, and protect it permanently.
• All uninfected, unprotected houses which have at least one infected neighbor become infected.

Cirno wants to stop the virus from spreading. Find the minimum number of houses that will be infected in the end, if she optimally choose the houses to protect.

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Note that every day Cirno always chooses a house to protect before the virus spreads. Also, a protected house will not be infected forever.

Input

The input consists of multiple test cases. The first line contains a single integer t$t$ (1≤t≤104$1\le t\le {10}^4$) — the number of test cases. Description of test cases follows.

The first line of each test case consists of two positive integers n,m$n,m$ (5≤n≤109$5\le n\le {10}^9$, 1≤m≤min(n,105)$1\le m\le min(n,{10}^5)$) — the number of houses on the circle, and the number of houses that are initially infected.

The second line of each test case consists of m$m$ distinct positive integers a1,a2,⋯,am$a_1,a_2,\cdots ,a_m$ (1≤ai≤n$1\le a_i\le n$) — the indices of the houses infected initially.

It is guaranteed that the sum of m$m$ over all test cases does not exceed 105${10}^5$.

Output

For each test case, output an integer on a separate line, which is the minimum number of infected houses in the end.