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 leng = (k - a[n-1]) + (a[0] - 0);
		int maxLeng = leng;
		for (int i = 0; i < n - 1; i++) {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		}
		System.out.println(leng - maxLeng);
		sc.close();
	}
} 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 leng = (k - a[n-1]) + (a[0] - 0);
		int maxLeng = leng;
		for (int i = 0; i < n - 1; i++) {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		}
		System.out.println(leng - maxLeng);
		sc.close();
	}
} 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 leng = (k - a[n-1]) + (a[0] - 0);
		int maxLeng = leng;
		for (int i = 0; i < n - 1; i++) {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		}
		System.out.println(leng - maxLeng);
		sc.close();
	} 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 leng = (k - a[n-1]) + (a[0] - 0);
		int maxLeng = leng;
		for (int i = 0; i < n - 1; i++) {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		}
		System.out.println(leng - maxLeng);
		sc.close();
	} 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 leng = (k - a[n-1]) + (a[0] - 0); leng (k - a[n-1]) + (a[0] - 0) (k - a[n-1]) k a[n-1] a n-1 n 1 (a[0] - 0) a[0] a 0 0 int maxLeng = leng; maxLeng leng for (int i = 0; i < n - 1; i++) {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		} int i = 0; int i = 0; i 0 i < n - 1 i n - 1 n 1 i++ i++ i {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		} {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		} int tmpLeng = a[i + 1] - a[i]; tmpLeng a[i + 1] - a[i] a[i + 1] a i + 1 i 1 a[i] a i leng += tmpLeng leng tmpLeng if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			} tmpLeng > maxLeng tmpLeng maxLeng {
				maxLeng = tmpLeng;
			} maxLeng = tmpLeng maxLeng tmpLeng System.out.println(leng - maxLeng) System.out.println System.out System System.out leng - maxLeng leng maxLeng sc.close() sc.close sc 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 leng = (k - a[n-1]) + (a[0] - 0);
		int maxLeng = leng;
		for (int i = 0; i < n - 1; i++) {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		}
		System.out.println(leng - maxLeng);
		sc.close();
	}
} 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 leng = (k - a[n-1]) + (a[0] - 0);
		int maxLeng = leng;
		for (int i = 0; i < n - 1; i++) {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		}
		System.out.println(leng - maxLeng);
		sc.close();
	}
} 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 leng = (k - a[n-1]) + (a[0] - 0);
		int maxLeng = leng;
		for (int i = 0; i < n - 1; i++) {
			int tmpLeng = a[i + 1] - a[i];
			leng += tmpLeng;
			if (tmpLeng > maxLeng) {
				maxLeng = tmpLeng;
			}
		}
		System.out.println(leng - maxLeng);
		sc.close();
	}
}