
import java.util.Scanner;

public class Main{
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int k = Integer.parseInt(sc.next());
		
		int n = Integer.parseInt(sc.next());
		
		int []a = new int [n];
		
		for(int i = 0 ; i < n ;i++) {
			a[i] = Integer.parseInt(sc.next());
		
		}
	
		int max = k-a[n-1]+ a[0];
		for(int i = 1 ;i < n ;i++) {
			max= Math.max(a[i] -a[i-1],max);	
		}
		

		System.out.println(k - max);
	}		
	} import java.util.Scanner; Scanner java.util public class Main{
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int k = Integer.parseInt(sc.next());
		
		int n = Integer.parseInt(sc.next());
		
		int []a = new int [n];
		
		for(int i = 0 ; i < n ;i++) {
			a[i] = Integer.parseInt(sc.next());
		
		}
	
		int max = k-a[n-1]+ a[0];
		for(int i = 1 ;i < n ;i++) {
			max= Math.max(a[i] -a[i-1],max);	
		}
		

		System.out.println(k - max);
	}		
	} Main public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int k = Integer.parseInt(sc.next());
		
		int n = Integer.parseInt(sc.next());
		
		int []a = new int [n];
		
		for(int i = 0 ; i < n ;i++) {
			a[i] = Integer.parseInt(sc.next());
		
		}
	
		int max = k-a[n-1]+ a[0];
		for(int i = 1 ;i < n ;i++) {
			max= Math.max(a[i] -a[i-1],max);	
		}
		

		System.out.println(k - max);
	} main {
		Scanner sc = new Scanner(System.in);
		
		int k = Integer.parseInt(sc.next());
		
		int n = Integer.parseInt(sc.next());
		
		int []a = new int [n];
		
		for(int i = 0 ; i < n ;i++) {
			a[i] = Integer.parseInt(sc.next());
		
		}
	
		int max = k-a[n-1]+ a[0];
		for(int i = 1 ;i < n ;i++) {
			max= Math.max(a[i] -a[i-1],max);	
		}
		

		System.out.println(k - max);
	} Scanner sc = new Scanner(System.in); sc new Scanner(System.in) int k = Integer.parseInt(sc.next()); k Integer.parseInt(sc.next()) Integer.parseInt Integer sc.next() sc.next sc int n = Integer.parseInt(sc.next()); n Integer.parseInt(sc.next()) Integer.parseInt Integer sc.next() sc.next sc int []a = new int [n]; a new int [n] n for(int i = 0 ; i < n ;i++) {
			a[i] = Integer.parseInt(sc.next());
		
		} int i = 0 ; int i = 0 ; i 0 i < n i n i++ i++ i {
			a[i] = Integer.parseInt(sc.next());
		
		} {
			a[i] = Integer.parseInt(sc.next());
		
		} a[i] = Integer.parseInt(sc.next()) a[i] a i Integer.parseInt(sc.next()) Integer.parseInt Integer sc.next() sc.next sc int max = k-a[n-1]+ a[0]; max k-a[n-1]+ a[0] k-a[n-1] k a[n-1] a n-1 n 1 a[0] a 0 for(int i = 1 ;i < n ;i++) {
			max= Math.max(a[i] -a[i-1],max);	
		} int i = 1 ; int i = 1 ; i 1 i < n i n i++ i++ i {
			max= Math.max(a[i] -a[i-1],max);	
		} {
			max= Math.max(a[i] -a[i-1],max);	
		} max= Math.max(a[i] -a[i-1],max) max Math.max(a[i] -a[i-1],max) Math.max Math a[i] -a[i-1] a[i] a i a[i-1] a i-1 i 1 max System.out.println(k - max) System.out.println System.out System System.out k - max k max String[] args args public class Main{
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int k = Integer.parseInt(sc.next());
		
		int n = Integer.parseInt(sc.next());
		
		int []a = new int [n];
		
		for(int i = 0 ; i < n ;i++) {
			a[i] = Integer.parseInt(sc.next());
		
		}
	
		int max = k-a[n-1]+ a[0];
		for(int i = 1 ;i < n ;i++) {
			max= Math.max(a[i] -a[i-1],max);	
		}
		

		System.out.println(k - max);
	}		
	} public class Main{
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int k = Integer.parseInt(sc.next());
		
		int n = Integer.parseInt(sc.next());
		
		int []a = new int [n];
		
		for(int i = 0 ; i < n ;i++) {
			a[i] = Integer.parseInt(sc.next());
		
		}
	
		int max = k-a[n-1]+ a[0];
		for(int i = 1 ;i < n ;i++) {
			max= Math.max(a[i] -a[i-1],max);	
		}
		

		System.out.println(k - max);
	}		
	} Main

import java.util.Scanner;

public class Main{
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int k = Integer.parseInt(sc.next());
		
		int n = Integer.parseInt(sc.next());
		
		int []a = new int [n];
		
		for(int i = 0 ; i < n ;i++) {
			a[i] = Integer.parseInt(sc.next());
		
		}
	
		int max = k-a[n-1]+ a[0];
		for(int i = 1 ;i < n ;i++) {
			max= Math.max(a[i] -a[i-1],max);	
		}
		

		System.out.println(k - max);
	}		
	}
