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 meter = 0;
	int maxmeter = a[0]+( k-a[n-1] );
	for(int i=0;i<n-1;i++){
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	}

	System.out.print(k-maxmeter);
    }
} 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 meter = 0;
	int maxmeter = a[0]+( k-a[n-1] );
	for(int i=0;i<n-1;i++){
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	}

	System.out.print(k-maxmeter);
    }
} 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 meter = 0;
	int maxmeter = a[0]+( k-a[n-1] );
	for(int i=0;i<n-1;i++){
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	}

	System.out.print(k-maxmeter);
    } 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 meter = 0;
	int maxmeter = a[0]+( k-a[n-1] );
	for(int i=0;i<n-1;i++){
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	}

	System.out.print(k-maxmeter);
    } 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 meter = 0; meter 0 int maxmeter = a[0]+( k-a[n-1] ); maxmeter 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++){
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	} int i=0; int i=0; i 0 i<n-1 i n-1 n 1 i++ i++ i {
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	} {
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	} meter = a[i+1]-a[i] meter a[i+1]-a[i] a[i+1] a i+1 i 1 a[i] a i if(meter > maxmeter) maxmeter = meter; meter > maxmeter meter maxmeter maxmeter = meter maxmeter meter System.out.print(k-maxmeter) System.out.print System.out System System.out k-maxmeter k maxmeter 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 meter = 0;
	int maxmeter = a[0]+( k-a[n-1] );
	for(int i=0;i<n-1;i++){
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	}

	System.out.print(k-maxmeter);
    }
} 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 meter = 0;
	int maxmeter = a[0]+( k-a[n-1] );
	for(int i=0;i<n-1;i++){
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	}

	System.out.print(k-maxmeter);
    }
} 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 meter = 0;
	int maxmeter = a[0]+( k-a[n-1] );
	for(int i=0;i<n-1;i++){
	    meter = a[i+1]-a[i];
	    if(meter > maxmeter) maxmeter = meter;
	}

	System.out.print(k-maxmeter);
    }
}
