import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);

        int K = Integer.parseInt(scan.next());
        int N = Integer.parseInt(scan.next());
        int min = 0;

        List<Integer> A = new ArrayList<>();
        List<Integer> dist = new ArrayList<>();

        for(int i=0; i<N; i++)
        {
            A.add(Integer.parseInt(scan.next()));
        }

        scan.close();
        
        for(int i=0; i<N; i++)
        {
            if(i<N-1)
            {
                dist.add(A.get(i+1) - A.get(i));
            }else{
                dist.add(K-A.get(i) + A.get(0));
            }
        }

        Collections.sort(dist);
        //System.out.println(dist);

        for(int i=0; i<N-1; i++)
        {
            min += dist.get(i);
        }
        System.out.println(min);
    }
}
/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