github.com/captn3m0/codechef.git

---
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---
<span class="solution-visible-txt">All submissions for this problem are available.</span>In a Circular City, there are $n$ houses, numbered from 1 to n and arranged in 1,2,...,n,1,2,...
Chef needs to deliver packages to $m$ (m<=n) houses. 

Chef is initially at house 1. Chef decides an integer $x$ and stops after every $x$ houses. i.e- if $n=7$ and $x=2$. He will stop at 1,3,5,7,2,... He may deliver a package when he stops at a house. His work is done when all the packages are delivered.

What is the minimum number of times Chef has to stop, if he can choose any $x$ ?

__Note__: Starting point (1) is also counted in number of stops

###Input:

- First line will contain $n, m$, denoting number of houses and number of packages respectively.
- Next line contains $m$ distinct space separated integers denoting the houses

###Output:
Single line containing an integer denoting minimum number of stops.

###Constraints 
- $3 \leq n \leq 1000$
- $1 \leq m \leq n$

###Sample Input 1:
	5 3
	1 2 4

###Sample Output 1:
	3

###Sample Input 2:
	6 2
	3 4

###Sample Output 2:
	4
	
###EXPLANATION:
For first input,
If Chef chooses $x=3$, he will stop at 1, 4, 2 before delivering all the packages.

For second,
If Chef chooses $x=1$, he will stop at 1, 2, 3, 4 before delivering all the packages.