import java.math.*;
import 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 max = A[0] + K - A[N - 1];
    for (int i = 1; i < N; i++)
      max = Integer.max(max, A[i] - A[i - 1]);

    long ans = K - max;
    System.out.println(ans);
  }
} import java.math.*; math.* java import java.util.*; util.* java 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 max = A[0] + K - A[N - 1];
    for (int i = 1; i < N; i++)
      max = Integer.max(max, A[i] - A[i - 1]);

    long ans = K - max;
    System.out.println(ans);
  }
} 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 max = A[0] + K - A[N - 1];
    for (int i = 1; i < N; i++)
      max = Integer.max(max, A[i] - A[i - 1]);

    long ans = K - max;
    System.out.println(ans);
  } 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 max = A[0] + K - A[N - 1];
    for (int i = 1; i < N; i++)
      max = Integer.max(max, A[i] - A[i - 1]);

    long ans = K - max;
    System.out.println(ans);
  } 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 max = A[0] + K - A[N - 1]; max A[0] + K - A[N - 1] A[0] + K A[0] A 0 K A[N - 1] A N - 1 N 1 for (int i = 1; i < N; i++)
      max = Integer.max(max, A[i] - A[i - 1]); int i = 1; int i = 1; i 1 i < N i N i++ i++ i max = Integer.max(max, A[i] - A[i - 1]); max = Integer.max(max, A[i] - A[i - 1]) max Integer.max(max, A[i] - A[i - 1]) Integer.max Integer max A[i] - A[i - 1] A[i] A i A[i - 1] A i - 1 i 1 long ans = K - max; ans K - max K max System.out.println(ans) System.out.println System.out System System.out ans 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 max = A[0] + K - A[N - 1];
    for (int i = 1; i < N; i++)
      max = Integer.max(max, A[i] - A[i - 1]);

    long ans = K - max;
    System.out.println(ans);
  }
} 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 max = A[0] + K - A[N - 1];
    for (int i = 1; i < N; i++)
      max = Integer.max(max, A[i] - A[i - 1]);

    long ans = K - max;
    System.out.println(ans);
  }
} Main
import java.math.*;
import 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 max = A[0] + K - A[N - 1];
    for (int i = 1; i < N; i++)
      max = Integer.max(max, A[i] - A[i - 1]);

    long ans = K - max;
    System.out.println(ans);
  }
}
