KIMO1  abdou set
Abdou has a set of unique positive integers. He wants to add several (possibly none) new positive integers to this set, such that when the set is sorted, for every two consecutive numbers X , Y abs(X%MY%M) = 1 . Your task is to calculate the smallest possible count of new numbers, with which he can achieve that.
Input
The first line contains T, the number of test cases. It is followed by 2*T lines, two lines per test case. The first line contains two positive integers M and N. The second line contains N integers.
1 <= T <= 5000 .
1 <= M <= 10^5
2 <= N <=50.
1 <= every integer in the set <= 10^6
Output
For test case print a single integer in a separate line: the smallest possible count of new numbers, with which he can complete the set or 1 if no solution exists.
Example
Input:
5
2 3
2 10 20
10 2
10 20
10 6
11 19 5 30 40 100
1 2
1 9999
15 3
4218 15210 1426
Output:
2
1
1
1
3
Explanation:
In the first test case we can add 3 and 13 to the given set to achieve abdou goal.
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SWOOSH!!!:
20130612 09:01:22
For the 3rd test case, shouldn't the solution be 11 12 13 14 15 16 17 18 19 8 7 6 5 4 3 2 1 30 41 40 101 100? Why is the output 1 then?


Mitch Schwartz:
20130610 00:50:17
A time limit of 0.029s makes AC in certain languages impossible because it is less than the interpreter startup time, e.g. on Cube a program that does nothing currently takes about 0.06s in Python 3 and 0.03s in Java. Please adjust the test data so that a more fair time limit such as 0.5s can be used.

Added by:  abdelkarim 
Date:  20130512 
Time limit:  0.5s 
Source limit:  5000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  owner 