import java.util.*;

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[] B = new int[N];
		for(int i=0; i < N-1; i++) {
			B[i] = A[i + 1] - A[i];
		}
		B[N-1] = A[0] + (K - A[N-1]);
		int sumB = 0;
		for(int i=0; i < N; i++) {
			sumB += B[i];
		}
		
		
		int maxL = 0;
		
		for(int i = 0; i < N; i++) {
			maxL = Math.max(maxL, B[i]);
		}


		System.out.println(sumB - maxL);

	}


}

 import java.util.*; util.* 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[] B = new int[N];
		for(int i=0; i < N-1; i++) {
			B[i] = A[i + 1] - A[i];
		}
		B[N-1] = A[0] + (K - A[N-1]);
		int sumB = 0;
		for(int i=0; i < N; i++) {
			sumB += B[i];
		}
		
		
		int maxL = 0;
		
		for(int i = 0; i < N; i++) {
			maxL = Math.max(maxL, B[i]);
		}


		System.out.println(sumB - maxL);

	}


} 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[] B = new int[N];
		for(int i=0; i < N-1; i++) {
			B[i] = A[i + 1] - A[i];
		}
		B[N-1] = A[0] + (K - A[N-1]);
		int sumB = 0;
		for(int i=0; i < N; i++) {
			sumB += B[i];
		}
		
		
		int maxL = 0;
		
		for(int i = 0; i < N; i++) {
			maxL = Math.max(maxL, B[i]);
		}


		System.out.println(sumB - maxL);

	} 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[] B = new int[N];
		for(int i=0; i < N-1; i++) {
			B[i] = A[i + 1] - A[i];
		}
		B[N-1] = A[0] + (K - A[N-1]);
		int sumB = 0;
		for(int i=0; i < N; i++) {
			sumB += B[i];
		}
		
		
		int maxL = 0;
		
		for(int i = 0; i < N; i++) {
			maxL = Math.max(maxL, B[i]);
		}


		System.out.println(sumB - maxL);

	} 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[] B = new int[N]; B new int[N] N for(int i=0; i < N-1; i++) {
			B[i] = A[i + 1] - A[i];
		} int i=0; int i=0; i 0 i < N-1 i N-1 N 1 i++ i++ i {
			B[i] = A[i + 1] - A[i];
		} {
			B[i] = A[i + 1] - A[i];
		} B[i] = A[i + 1] - A[i] B[i] B i A[i + 1] - A[i] A[i + 1] A i + 1 i 1 A[i] A i B[N-1] = A[0] + (K - A[N-1]) B[N-1] B N-1 N 1 A[0] + (K - A[N-1]) A[0] A 0 (K - A[N-1]) K A[N-1] A N-1 N 1 int sumB = 0; sumB 0 for(int i=0; i < N; i++) {
			sumB += B[i];
		} int i=0; int i=0; i 0 i < N i N i++ i++ i {
			sumB += B[i];
		} {
			sumB += B[i];
		} sumB += B[i] sumB B[i] B i int maxL = 0; maxL 0 for(int i = 0; i < N; i++) {
			maxL = Math.max(maxL, B[i]);
		} int i = 0; int i = 0; i 0 i < N i N i++ i++ i {
			maxL = Math.max(maxL, B[i]);
		} {
			maxL = Math.max(maxL, B[i]);
		} maxL = Math.max(maxL, B[i]) maxL Math.max(maxL, B[i]) Math.max Math maxL B[i] B i System.out.println(sumB - maxL) System.out.println System.out System System.out sumB - maxL sumB maxL String[] args args
import java.util.*;

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[] B = new int[N];
		for(int i=0; i < N-1; i++) {
			B[i] = A[i + 1] - A[i];
		}
		B[N-1] = A[0] + (K - A[N-1]);
		int sumB = 0;
		for(int i=0; i < N; i++) {
			sumB += B[i];
		}
		
		
		int maxL = 0;
		
		for(int i = 0; i < N; i++) {
			maxL = Math.max(maxL, B[i]);
		}


		System.out.println(sumB - maxL);

	}


}


