import java.util.*;
public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
  	long k=sc.nextLong();
  	int n=sc.nextInt();
  	long[] ai=new long[n];
  	for(int i=0;i<n;i++){
  		ai[i]=sc.nextLong();
  	}
  	long s=0;
  	long[] si=new long[n];
  	for(int i=0;i<n;i++){
  		if(i==n-1){
  			si[i]=k+ai[0]-ai[i];
  		}else{
  			si[i]=ai[i+1]-ai[i];
  		}
  	}
  	Arrays.sort(si);
  	for(int i=0;i<n-1;i++){
  		s+=si[i];
  	}
  	System.out.print(s);
  }
}
/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