import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author maheshwari29
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTravelingSalesmanAroundLake {
        static void merge(long arr[], int l, int m, int r) {
            int n1 = m - l + 1;
            int n2 = r - m;
            long L[] = new long[n1];
            long R[] = new long[n2];
            for (int i = 0; i < n1; ++i) L[i] = arr[l + i];
            for (int j = 0; j < n2; ++j) R[j] = arr[m + 1 + j];
            int i = 0, j = 0;
            int k = l;
            while (i < n1 && j < n2) {
                if (L[i] <= R[j]) {
                    arr[k] = L[i];
                    i++;
                } else {
                    arr[k] = R[j];
                    j++;
                }
                k++;
            }
            while (i < n1) {
                arr[k] = L[i];
                i++;
                k++;
            }
            while (j < n2) {
                arr[k] = R[j];
                j++;
                k++;
            }
        }

        static void Sort(long arr[], int l, int r) {
            if (l < r) {
                int m = (l + r) / 2;
                Sort(arr, l, m);
                Sort(arr, m + 1, r);
                merge(arr, l, m, r);
            }
        }

        static void sort(long a[]) {
            Sort(a, 0, a.length - 1);
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int i, j;
            int k = in.ni();
            int n = in.ni();
            long a[] = in.nla(n);
            sort(a);
            long sum = 0;
            for (long c : a)
                sum += c;
            long max = 0;
            for (i = 0; i < n - 1; i++)
                max = Math.max(max, a[i + 1] - a[i]);
            long temp = k - a[n - 1] + a[0];
            //out.println(temp);
            max = Math.max(max, temp);
            //out.println(max);
            out.println(k - max);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public long[] nla(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; ++i) array[i] = nl();
            return array;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}



Measured memory_bytes: 48348