// package app;

import java.math.BigDecimal;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.Scanner;
import java.util.StringJoiner;
import java.util.stream.Stream;

public class Main {

    public static void main(final String[] args) throws Exception {

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

        int ans = K - max;
        System.out.println(ans);
    }
} import java.math.BigDecimal; BigDecimal java.math import java.util.ArrayList; ArrayList java.util import java.util.Arrays; Arrays java.util import java.util.Collections; Collections java.util import java.util.HashMap; HashMap java.util import java.util.List; List java.util import java.util.Map; Map java.util import java.util.Objects; Objects java.util import java.util.Scanner; Scanner java.util import java.util.StringJoiner; StringJoiner java.util import java.util.stream.Stream; Stream java.util.stream public class Main {

    public static void main(final String[] args) throws Exception {

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

        int ans = K - max;
        System.out.println(ans);
    }
} Main public static void main(final String[] args) throws Exception {

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

        int 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();
        }

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

        int 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] = sc.nextInt() A[i] A i sc.nextInt() sc.nextInt 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(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 int ans = K - max; ans K - max K max System.out.println(ans) System.out.println System.out System System.out ans final String[] args args public class Main {

    public static void main(final String[] args) throws Exception {

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

        int ans = K - max;
        System.out.println(ans);
    }
} public class Main {

    public static void main(final String[] args) throws Exception {

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

        int ans = K - max;
        System.out.println(ans);
    }
} Main
// package app;

import java.math.BigDecimal;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.Scanner;
import java.util.StringJoiner;
import java.util.stream.Stream;

public class Main {

    public static void main(final String[] args) throws Exception {

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

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