import java.util.Scanner;


public 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 = (K - A[N-1]) + A[0];
		for (int i = 1; i < N; i++) {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
		}
		System.out.println(K - max);
	}
} import java.util.Scanner; Scanner java.util public 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 = (K - A[N-1]) + A[0];
		for (int i = 1; i < N; i++) {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
		}
		System.out.println(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 = (K - A[N-1]) + A[0];
		for (int i = 1; i < N; i++) {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
		}
		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();
		int max = (K - A[N-1]) + A[0];
		for (int i = 1; i < N; i++) {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
		}
		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] A i sc.nextInt() sc.nextInt sc int max = (K - A[N-1]) + A[0]; max (K - A[N-1]) + A[0] (K - A[N-1]) K A[N-1] A N-1 N 1 A[0] A 0 for (int i = 1; i < N; i++) {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
		} int i = 1; int i = 1; i 1 i < N i N i++ i++ i {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
		} {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
		} int m = A[i] - A[i-1]; m A[i] - A[i-1] A[i] A i A[i-1] A i-1 i 1 if (max < m) max = m; max < m max m max = m max m 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) {
		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 = (K - A[N-1]) + A[0];
		for (int i = 1; i < N; i++) {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
		}
		System.out.println(K - max);
	}
} public 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 = (K - A[N-1]) + A[0];
		for (int i = 1; i < N; i++) {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
		}
		System.out.println(K - max);
	}
} Main
import java.util.Scanner;


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