Rikka with wood sticks

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:


Yuta have a wood stick of length $n$ which consists of $n$ linked sticks of length $1$. So it has $n-1$ connection points. Yuta finds that some sticks of length $1$ of the wood stick are not strong. So he wants to choose three different connection points to cut it into four wood sticks and only one of them contains wood sticks which are not strong. And Yuta wants to minimize the length of this piece which contains bad wood sticks. Besides, Rikka wants to use the other three wood sticks to make a triangle. Now she wants to count the number of the ways to cut the wood sticks which can make both Yuta and herself happy.


It is too difficult for Rikka. Can you help her?

This problem has multi test cases (no more than $20$). For each test case, The first line contains two numbers $n,m(1 \leq n \leq 1000000,1 \leq m \leq 1000)$. The next line contains m numbers (some of them may be same) – the position of each wood sticks which is not strong.

For each test cases print only one number – the ways to cut the wood sticks.

6 1
3
5 1
3

2
0

BestCoder Round #37 ($)