import java.util.*;

class Main{
	static public void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int k=sc.nextInt();
		int n=sc.nextInt();
		int ans=0;
		int[] an=new int[n+1];
		
		for(int i=0;i<n;i++){
			an[i]=sc.nextInt();
		}
		an[n]=an[0]+k;
		for(int i=0;i<n;i++){
			ans=Math.max(ans,an[i+1]-an[i]);
		}
		int aa=k-ans;
		System.out.println(aa);
	}
}
/tmp/hf-datasets-cache/medium/datasets/42704881117311-config-parquet-and-info-qiankunmu-Project_CodeNet-896c9d36/hub/datasets--qiankunmu--Project_CodeNet_Python800_and_Java250/snapshots/c899fde44a77ba1cc14973ed3de064e4ff3aadc7/Project_CodeNet_Java250.tar.gz