All submissions for this problem are available.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.
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
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