import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (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 max = (K + A[0]) - A[N - 1];
            for (int i = 1; i < N; i++) {
                max = Math.max(max, A[i] - A[i - 1]);
            }

            System.out.println(K - max);
        }
    }
} import java.util.Scanner; Scanner java.util public class Main {
    public static void main(String[] args) {
        try (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 max = (K + A[0]) - A[N - 1];
            for (int i = 1; i < N; i++) {
                max = Math.max(max, A[i] - A[i - 1]);
            }

            System.out.println(K - max);
        }
    }
} Main public static void main(String[] args) {
        try (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 max = (K + A[0]) - A[N - 1];
            for (int i = 1; i < N; i++) {
                max = Math.max(max, A[i] - A[i - 1]);
            }

            System.out.println(K - max);
        }
    } main {
        try (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 max = (K + A[0]) - A[N - 1];
            for (int i = 1; i < N; i++) {
                max = Math.max(max, A[i] - A[i - 1]);
            }

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

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

            System.out.println(K - max);
        } Scanner sc = new Scanner(System.in) Scanner sc = new Scanner(System.in) 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 max = (K + A[0]) - A[N - 1]; max (K + A[0]) - A[N - 1] (K + A[0]) K A[0] A 0 A[N - 1] A N - 1 N 1 for (int i = 1; i < N; i++) {
                max = Math.max(max, A[i] - A[i - 1]);
            } int i = 1; int i = 1; i 1 i < N i N i++ i++ i {
                max = Math.max(max, A[i] - A[i - 1]);
            } {
                max = Math.max(max, A[i] - A[i - 1]);
            } max = Math.max(max, A[i] - A[i - 1]) max Math.max(max, A[i] - A[i - 1]) Math.max Math max A[i] - A[i - 1] A[i] A i A[i - 1] A i - 1 i 1 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) {
        try (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 max = (K + A[0]) - A[N - 1];
            for (int i = 1; i < N; i++) {
                max = Math.max(max, A[i] - A[i - 1]);
            }

            System.out.println(K - max);
        }
    }
} public class Main {
    public static void main(String[] args) {
        try (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 max = (K + A[0]) - A[N - 1];
            for (int i = 1; i < N; i++) {
                max = Math.max(max, A[i] - A[i - 1]);
            }

            System.out.println(K - max);
        }
    }
} Main
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (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 max = (K + A[0]) - A[N - 1];
            for (int i = 1; i < N; i++) {
                max = Math.max(max, A[i] - A[i - 1]);
            }

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