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

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

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

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

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

}