import java.util.Scanner;

public class Main {

	public static void main(final 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();
		}
		sc.close();
		int max = 0;;
		for(int i = 0; i < N - 1; i++) {
			max = Math.max(max, A[i + 1] - A[i]);
		}
		max = Math.max(max, K - A[N - 1] + A[0]);
		System.out.println(K - max);
	}
} import java.util.Scanner; Scanner java.util public class Main {

	public static void main(final 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();
		}
		sc.close();
		int max = 0;;
		for(int i = 0; i < N - 1; i++) {
			max = Math.max(max, A[i + 1] - A[i]);
		}
		max = Math.max(max, K - A[N - 1] + A[0]);
		System.out.println(K - max);
	}
} Main public static void main(final 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();
		}
		sc.close();
		int max = 0;;
		for(int i = 0; i < N - 1; i++) {
			max = Math.max(max, A[i + 1] - A[i]);
		}
		max = Math.max(max, K - A[N - 1] + A[0]);
		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();
		}
		sc.close();
		int max = 0;;
		for(int i = 0; i < N - 1; i++) {
			max = Math.max(max, A[i + 1] - A[i]);
		}
		max = Math.max(max, K - A[N - 1] + A[0]);
		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 sc.close() sc.close sc int max = 0; max 0 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 max = Math.max(max, K - A[N - 1] + A[0]) max Math.max(max, K - A[N - 1] + A[0]) Math.max Math max K - A[N - 1] + A[0] K - A[N - 1] K A[N - 1] A N - 1 N 1 A[0] A 0 System.out.println(K - max) System.out.println System.out System System.out K - max K max final String[] args args public class Main {

	public static void main(final 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();
		}
		sc.close();
		int max = 0;;
		for(int i = 0; i < N - 1; i++) {
			max = Math.max(max, A[i + 1] - A[i]);
		}
		max = Math.max(max, K - A[N - 1] + A[0]);
		System.out.println(K - max);
	}
} public class Main {

	public static void main(final 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();
		}
		sc.close();
		int max = 0;;
		for(int i = 0; i < N - 1; i++) {
			max = Math.max(max, A[i + 1] - A[i]);
		}
		max = Math.max(max, K - A[N - 1] + A[0]);
		System.out.println(K - max);
	}
} Main
import java.util.Scanner;

public class Main {

	public static void main(final 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();
		}
		sc.close();
		int max = 0;;
		for(int i = 0; i < N - 1; i++) {
			max = Math.max(max, A[i + 1] - A[i]);
		}
		max = Math.max(max, K - A[N - 1] + A[0]);
		System.out.println(K - max);
	}
}