Problem:
Score : 300 points

Problem Statement

There is a circular pond with a perimeter of K meters, and N houses around them.

The i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.

When traveling between these houses, you can only go around the pond.

Find the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Constraints

2 \leq K \leq 10^6

2 \leq N \leq 2 \times 10^5

0 \leq A_1 < ... < A_N < K

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K N
A_1 A_2 ... A_N

Output

Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Sample Input 1

20 3
5 10 15

Sample Output 1

10

If you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.

Sample Input 2

20 3
0 5 15

Sample Output 2

10

If you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main implements Runnable {


    long m = (int)1e9+7;
    PrintWriter rw;
    ArrayList<Integer> prime;
    boolean is_prime[];
    InputReader sc;
    public void run() {
        sc = new InputReader(System.in);
        rw = new PrintWriter(System.out);

        int k = sc.nextInt();
        int n = sc.nextInt();
        int[] a = scanArrayI(n);
        int dist = a[n-1] - a[0];
        for(int i = 1; i < n; i++){
            dist = (Math.min(dist, (k-a[i]) + a[i-1]));
        }
        rw.println(dist);
        rw.close();
    }

    public long prob(long n){
        return n * (n-1) / 2;
    }

    private static int maxIndex(List<Integer> list) {
        Integer i=0, maxIndex=-1, max=null;
        for (Integer x : list) {
            if ((x!=null) && ((max==null) || (x>max))) {
                max = x;
                maxIndex = i;
            }
            i++;
        }
        return maxIndex;
    }

    static int largest(int[] arr) {
        int i;
        int max = arr[0];
        for (i = 1; i < arr.length; i++)
            if (arr[i] > max)
                max = arr[i];
        return max;
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    void sieve(int n) {
        is_prime = new boolean[n+10];
        prime = new ArrayList<>();
        for(int i=2;i<=n;i++)
            is_prime[i] = true;

        for (int i = 2; i <= n; ++i) {
            if (is_prime[i]) prime.add(i);
            for (int j = 0; j < prime.size () && i * prime.get(j) < n; ++j) {
                is_prime[i * prime.get(j)] = false;
                if (i % prime.get(j) == 0) break;
            }
        }
    }
    public static void sortbyColumn(int arr[][], int col){
        Arrays.sort(arr, new Comparator<int[]>()
        {
            public int compare(int[] o1, int[] o2){
                return(Integer.valueOf(o1[col]).compareTo(o2[col]));
            }
        });

    }
    public static class DJSet {
        public int[] upper;

        public DJSet(int n) {
            upper = new int[n];
            Arrays.fill(upper, -1);
        }

        public int root(int x) {
            return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
        }

        public boolean equiv(int x, int y) {
            return root(x) == root(y);
        }

        public boolean union(int x, int y) {
            x = root(x);
            y = root(y);
            if (x != y) {
                if (upper[y] < upper[x]) {
                    int d = x;
                    x = y;
                    y = d;
                }
                upper[x] += upper[y];
                upper[y] = x;
            }
            return x == y;
        }
    }
    public static int[] radixSort(int[] f)    {
        int[] to = new int[f.length];
        {
            int[] b = new int[65537];
            for(int i = 0;i < f.length;i++)b[1+(f[i]&0xffff)]++;
            for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
            for(int i = 0;i < f.length;i++)to[b[f[i]&0xffff]++] = f[i];
            int[] d = f; f = to;to = d;
        }
        {
            int[] b = new int[65537];
            for(int i = 0;i < f.length;i++)b[1+(f[i]>>>16)]++;
            for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
            for(int i = 0;i < f.length;i++)to[b[f[i]>>>16]++] = f[i];
            int[] d = f; f = to;to = d;
        }
        return f;
    }


    public void printArray(int[] a){
        for(int i=0;i<a.length;i++)
            rw.print(a[i]+"");
        rw.println();
    }
    public int[] scanArrayI(int n){
        int[] a = new int[n];
        for(int i=0;i<n;i++)
            a[i] = sc.nextInt();
        return a;
    }

    public int[][] scan2dArrayI(int n, int m){
        int [][] a = new int[n][m];
        for(int i = 0; i < n; i++){
            for(int j = 0; j < m; j++){
                a[i][j] = sc.nextInt();
            }
        }
        return  a;
    }
    public void print2dArrayI(int[][] a){
        for(int i = 0; i < a.length; i++){
            for(int j = 0; j < a.length; j++){
                rw.print(a[i][j] + " ");
            }
            rw.println();
        }
    }
    public long[] scanArrayL(int n){
        long[] a = new long[n];
        for(int i=0;i<n;i++)
            a[i] = sc.nextLong();
        return a;
    }
    public void printArray(long[] a){
        for(int i=0;i<a.length;i++)
            rw.print(a[i]+" ");
        rw.println();
    }
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            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 nextLong() {
            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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(),"Main",1<<26).start();
    }
}