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 X = 0;
		int Y = A[0]+(k-A[N-1]);
		for(int i=0; i<N-1; i++) {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		}
		System.out.print(k-Y);
	}
} 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 X = 0;
		int Y = A[0]+(k-A[N-1]);
		for(int i=0; i<N-1; i++) {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		}
		System.out.print(k-Y);
	}
} 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 X = 0;
		int Y = A[0]+(k-A[N-1]);
		for(int i=0; i<N-1; i++) {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		}
		System.out.print(k-Y);
	} 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 X = 0;
		int Y = A[0]+(k-A[N-1]);
		for(int i=0; i<N-1; i++) {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		}
		System.out.print(k-Y);
	} 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 X = 0; X 0 int Y = A[0]+(k-A[N-1]); Y 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++) {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		} int i=0; int i=0; i 0 i<N-1 i N-1 N 1 i++ i++ i {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		} {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		} X = A[i+1]-A[i] X A[i+1]-A[i] A[i+1] A i+1 i 1 A[i] A i if(X>=Y) {
			Y = X;
		} X>=Y X Y {
			Y = X;
		} Y = X Y X System.out.print(k-Y) System.out.print System.out System System.out k-Y k Y 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 X = 0;
		int Y = A[0]+(k-A[N-1]);
		for(int i=0; i<N-1; i++) {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		}
		System.out.print(k-Y);
	}
} 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 X = 0;
		int Y = A[0]+(k-A[N-1]);
		for(int i=0; i<N-1; i++) {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		}
		System.out.print(k-Y);
	}
} 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 X = 0;
		int Y = A[0]+(k-A[N-1]);
		for(int i=0; i<N-1; i++) {
			X = A[i+1]-A[i];
		if(X>=Y) {
			Y = X;
		}	
		}
		System.out.print(k-Y);
	}
}