import java.util.*;

public class Main{
  public static void main(String[] args) {
    Scanner sc=new Scanner(System.in);
    int k=sc.nextInt();
    int n=sc.nextInt();
    int a[]=new int[n+1];
    for (int i=0;i<n;i++) {
      a[i]=sc.nextInt();
    }
    a[n]=k+a[0]-a[n-1];

    for (int i=n-1;i>0;i--) {
      a[i]=a[i]-a[i-1];
      // System.out.println(a[i]);
    }

    Arrays.sort(a);


    System.out.println(k-a[n]);
  }
}

/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