import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int K = sc.nextInt();
        int N = sc.nextInt();
        
        int[] A =new int[N];
        
        for(int i=0;i<N;i++){
            A[i]=sc.nextInt();
        }
        long max =A[0]+(K-A[N-1]);
        
        for(int i=0;i<N-1;i++){
            max = Math.max(max, A[i+1]-A[i]);
        }
        System.out.println(K-max);
        
    }
} import java.util.*; util.* java public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int K = sc.nextInt();
        int N = sc.nextInt();
        
        int[] A =new int[N];
        
        for(int i=0;i<N;i++){
            A[i]=sc.nextInt();
        }
        long max =A[0]+(K-A[N-1]);
        
        for(int i=0;i<N-1;i++){
            max = Math.max(max, A[i+1]-A[i]);
        }
        System.out.println(K-max);
        
    }
} Main public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int K = sc.nextInt();
        int N = sc.nextInt();
        
        int[] A =new int[N];
        
        for(int i=0;i<N;i++){
            A[i]=sc.nextInt();
        }
        long max =A[0]+(K-A[N-1]);
        
        for(int i=0;i<N-1;i++){
            max = Math.max(max, A[i+1]-A[i]);
        }
        System.out.println(K-max);
        
    } main {
        Scanner sc = new Scanner(System.in);
        int K = sc.nextInt();
        int N = sc.nextInt();
        
        int[] A =new int[N];
        
        for(int i=0;i<N;i++){
            A[i]=sc.nextInt();
        }
        long max =A[0]+(K-A[N-1]);
        
        for(int i=0;i<N-1;i++){
            max = Math.max(max, A[i+1]-A[i]);
        }
        System.out.println(K-max);
        
    } Scanner sc = new Scanner(System.in); sc new Scanner(System.in) int K = sc.nextInt(); K sc.nextInt() sc.nextInt sc int N = sc.nextInt(); N sc.nextInt() sc.nextInt sc int[] A =new int[N]; A new int[N] N for(int i=0;i<N;i++){
            A[i]=sc.nextInt();
        } int i=0; int i=0; i 0 i<N i N i++ i++ i {
            A[i]=sc.nextInt();
        } {
            A[i]=sc.nextInt();
        } A[i]=sc.nextInt() A[i] A i sc.nextInt() sc.nextInt sc long max =A[0]+(K-A[N-1]); max A[0]+(K-A[N-1]) A[0] A 0 (K-A[N-1]) K A[N-1] A N-1 N 1 for(int i=0;i<N-1;i++){
            max = Math.max(max, A[i+1]-A[i]);
        } int i=0; int i=0; i 0 i<N-1 i N-1 N 1 i++ i++ i {
            max = Math.max(max, A[i+1]-A[i]);
        } {
            max = Math.max(max, A[i+1]-A[i]);
        } max = Math.max(max, A[i+1]-A[i]) max Math.max(max, A[i+1]-A[i]) Math.max Math max A[i+1]-A[i] A[i+1] A i+1 i 1 A[i] A i System.out.println(K-max) System.out.println System.out System System.out K-max K max String[] args args public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int K = sc.nextInt();
        int N = sc.nextInt();
        
        int[] A =new int[N];
        
        for(int i=0;i<N;i++){
            A[i]=sc.nextInt();
        }
        long max =A[0]+(K-A[N-1]);
        
        for(int i=0;i<N-1;i++){
            max = Math.max(max, A[i+1]-A[i]);
        }
        System.out.println(K-max);
        
    }
} public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int K = sc.nextInt();
        int N = sc.nextInt();
        
        int[] A =new int[N];
        
        for(int i=0;i<N;i++){
            A[i]=sc.nextInt();
        }
        long max =A[0]+(K-A[N-1]);
        
        for(int i=0;i<N-1;i++){
            max = Math.max(max, A[i+1]-A[i]);
        }
        System.out.println(K-max);
        
    }
} Main
import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int K = sc.nextInt();
        int N = sc.nextInt();
        
        int[] A =new int[N];
        
        for(int i=0;i<N;i++){
            A[i]=sc.nextInt();
        }
        long max =A[0]+(K-A[N-1]);
        
        for(int i=0;i<N-1;i++){
            max = Math.max(max, A[i+1]-A[i]);
        }
        System.out.println(K-max);
        
    }
}
