import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		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[] amari = new int[N];

		for(int i=1; i<N; i++) {
			amari[i] = A[i] - A[i-1];
		}
		amari[0] = (K - A[N-1]) + A[0];

		Arrays.sort(amari);

		int ans = K - amari[N-1];

		System.out.println(ans);
	}

} import java.util.Arrays; Arrays java.util import java.util.Scanner; Scanner java.util public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		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[] amari = new int[N];

		for(int i=1; i<N; i++) {
			amari[i] = A[i] - A[i-1];
		}
		amari[0] = (K - A[N-1]) + A[0];

		Arrays.sort(amari);

		int ans = K - amari[N-1];

		System.out.println(ans);
	}

} Main public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		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[] amari = new int[N];

		for(int i=1; i<N; i++) {
			amari[i] = A[i] - A[i-1];
		}
		amari[0] = (K - A[N-1]) + A[0];

		Arrays.sort(amari);

		int ans = K - amari[N-1];

		System.out.println(ans);
	} main {
		// TODO 自動生成されたメソッド・スタブ
		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[] amari = new int[N];

		for(int i=1; i<N; i++) {
			amari[i] = A[i] - A[i-1];
		}
		amari[0] = (K - A[N-1]) + A[0];

		Arrays.sort(amari);

		int ans = K - amari[N-1];

		System.out.println(ans);
	} 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[] amari = new int[N]; amari new int[N] N for(int i=1; i<N; i++) {
			amari[i] = A[i] - A[i-1];
		} int i=1; int i=1; i 1 i<N i N i++ i++ i {
			amari[i] = A[i] - A[i-1];
		} {
			amari[i] = A[i] - A[i-1];
		} amari[i] = A[i] - A[i-1] amari[i] amari i A[i] - A[i-1] A[i] A i A[i-1] A i-1 i 1 amari[0] = (K - A[N-1]) + A[0] amari[0] amari 0 (K - A[N-1]) + A[0] (K - A[N-1]) K A[N-1] A N-1 N 1 A[0] A 0 Arrays.sort(amari) Arrays.sort Arrays amari int ans = K - amari[N-1]; ans K - amari[N-1] K amari[N-1] amari N-1 N 1 System.out.println(ans) System.out.println System.out System System.out ans String[] args args public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		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[] amari = new int[N];

		for(int i=1; i<N; i++) {
			amari[i] = A[i] - A[i-1];
		}
		amari[0] = (K - A[N-1]) + A[0];

		Arrays.sort(amari);

		int ans = K - amari[N-1];

		System.out.println(ans);
	}

} public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		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[] amari = new int[N];

		for(int i=1; i<N; i++) {
			amari[i] = A[i] - A[i-1];
		}
		amari[0] = (K - A[N-1]) + A[0];

		Arrays.sort(amari);

		int ans = K - amari[N-1];

		System.out.println(ans);
	}

} Main
import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		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[] amari = new int[N];

		for(int i=1; i<N; i++) {
			amari[i] = A[i] - A[i-1];
		}
		amari[0] = (K - A[N-1]) + A[0];

		Arrays.sort(amari);

		int ans = K - amari[N-1];

		System.out.println(ans);
	}

}
