import java.util.*;
import java.math.*;

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];
        for(int i = 0; i < N; i++){
            A[i] = sc.nextInt();
        }
        int max = A[0] - A[N - 1] + K;
        for(int i = 0; i < N - 1; i++){
            if(max < A[i + 1] - A[i]){
                max = A[i + 1] - A[i];
            }
        }
        System.out.print(K - max);
	}

} import java.util.*; util.* java import java.math.*; math.* java 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];
        for(int i = 0; i < N; i++){
            A[i] = sc.nextInt();
        }
        int max = A[0] - A[N - 1] + K;
        for(int i = 0; i < N - 1; i++){
            if(max < A[i + 1] - A[i]){
                max = A[i + 1] - A[i];
            }
        }
        System.out.print(K - max);
	}

} 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];
        for(int i = 0; i < N; i++){
            A[i] = sc.nextInt();
        }
        int max = A[0] - A[N - 1] + K;
        for(int i = 0; i < N - 1; i++){
            if(max < A[i + 1] - A[i]){
                max = A[i + 1] - A[i];
            }
        }
        System.out.print(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();
        }
        int max = A[0] - A[N - 1] + K;
        for(int i = 0; i < N - 1; i++){
            if(max < A[i + 1] - A[i]){
                max = A[i + 1] - A[i];
            }
        }
        System.out.print(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 int max = A[0] - A[N - 1] + K; max A[0] - A[N - 1] + K A[0] - A[N - 1] A[0] A 0 A[N - 1] A N - 1 N 1 K for(int i = 0; i < N - 1; i++){
            if(max < A[i + 1] - A[i]){
                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 {
            if(max < A[i + 1] - A[i]){
                max = A[i + 1] - A[i];
            }
        } {
            if(max < A[i + 1] - A[i]){
                max = A[i + 1] - A[i];
            }
        } if(max < A[i + 1] - A[i]){
                max = A[i + 1] - A[i];
            } max < A[i + 1] - A[i] max A[i + 1] - A[i] A[i + 1] A i + 1 i 1 A[i] A i {
                max = A[i + 1] - A[i];
            } max = A[i + 1] - A[i] max A[i + 1] - A[i] A[i + 1] A i + 1 i 1 A[i] A i System.out.print(K - max) System.out.print System.out System System.out K - max K max String[] args args
import java.util.*;
import java.math.*;

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];
        for(int i = 0; i < N; i++){
            A[i] = sc.nextInt();
        }
        int max = A[0] - A[N - 1] + K;
        for(int i = 0; i < N - 1; i++){
            if(max < A[i + 1] - A[i]){
                max = A[i + 1] - A[i];
            }
        }
        System.out.print(K - max);
	}

}