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.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Random;

/**
 *  @author Ivan Pryvalov (ivan.pryvalov@gmail.com)
 */
public class Main implements Runnable {

    static EventType eventType = EventType.DEFAULT; //EventType.GOOGLE_CODE_JAM;
    static boolean interactive = false; //use outGlobal.println()   and   outGlobal.flush()
    static int T = 1; // T \in {0,1}. If T=0, it will be read from the input.
    static String inputFilename = null; // if 'null', it reads data from std-in.

    static boolean largeFakeTest = false; // Check if you generate data on fly
    static int largeFakeTest_T = 1;
    //--------------------------------------------------------------------



    public static class Solver extends  SolverAbstract{

        int K,N;
        int[] A;

        @Override
        public void readInput() throws IOException {
            K = scanner.nextInt();
            N = scanner.nextInt();
            A = scanner.loadIntArray(N);
        }

        @Override
        protected void solve() throws IOException {
            int maxDist = 0;
            for (int i = 1; i < N; i++) {
                maxDist = Math.max(maxDist, A[i]-A[i-1]);
            }
            maxDist = Math.max(maxDist, (K+A[0]) - A[N-1]);
            out.println(K-maxDist);
        }

    }

    //--------------------------------------------------------------------

    private void solveAll() throws IOException {
        long timeStart = System.currentTimeMillis();
        if (T==0) {
            if (largeFakeTest) {
                T = largeFakeTest_T;
            } else {
                T = scanner.nextInt();
            }
        }
        final String[] results = new String[T+1];
        for (int test = 0; test < T; test++) {
            ByteArrayOutputStream baos = new ByteArrayOutputStream();
            PrintStream outLocal = new PrintStream(baos);
            Solver solver = new Solver(){
                @Override
                public void callback() {
                    results[testNo] = answer;
                }
            };
            solver.out = outLocal;
            solver.testNo = test+1;
            if (largeFakeTest) {
                solver.readFakeInput();
            }else{
                solver.readInput();
            }
            solver.solveWrapped(baos);
        }

        long timeEnd = System.currentTimeMillis();
        if (isInputFromFile())
            System.out.println("All tasks are solved! Elapsed time "+(timeEnd-timeStart)/1000.0+" sec.");

        // write all responses in the proper order
        if (!interactive) {
            for (int i = 1; i <= T; i++) {
                if (eventType == EventType.GOOGLE_CODE_JAM) {
                    outGlobal.printf("Case #%d: %s", i, results[i]);
                } else {
                    outGlobal.print(results[i]);
                }
            }
        }
    }

    enum EventType{
        DEFAULT,
        GOOGLE_CODE_JAM
    }

    static boolean isInputFromFile() {
        return inputFilename != null;
    }

    public static abstract class SolverAbstract {
        PrintStream out;
        int testNo;
        String answer = null;

        public void callback(){};

        public abstract void readInput() throws IOException;

        //generate a randomized test with the maximal input values
        public void readFakeInput() throws  IOException{
            throw new RuntimeException("not implemented");
        }

        protected abstract void solve() throws IOException;

        protected void solveWrapped(ByteArrayOutputStream baos) throws IOException {
            if (isInputFromFile())
                System.out.println("SOLVER: solving task #"+testNo+" out of "+ T+"...");
            solve();
            answer = baos.toString();
            if (isInputFromFile()) {
                System.out.println("\t"+answer);
            }
            callback();
        }
    }

    ////////////////////////////////////////////////////////
    // Link about multithreading: http://stackoverflow.com/questions/4521983/java-executorservice-that-blocks-on-submission-after-a-certain-queue-size


    // ------------- Some stardard tools that are currently not tested.
    //adopt for the lists of adjacent vertices
    static class Graph{

        int[][] G;
        int N;

        int[][] A;
        int[][] F;

        int[] path;
        int pathLen;
        boolean[] visited;
        int target;
        boolean flowFound;

        public Graph(int[][] g) {
            G = g;
            N = G.length;
        }

        public int[][] maxflow(int iSource, int iSink) {
            path = new int[N];
            visited = new boolean[N];

            A = new int[N][];
            for (int i = 0; i < N; i++) {
                A[i] = G[i].clone();
            }
            F = new int[N][N];

            target = iSink;
            //dfs from source to sink
            //increase path
            while(true){
                flowFound = false;
                visited[iSource] = true;
                pathLen = 0;
                path[pathLen++] = iSource;
                dfs(iSource);
                if (!flowFound)
                    break;
            }
            return F;
        }

        private void dfs(int u) {
            if (u==target){
                flowFound = true;
                for (int i = 0; i < pathLen-1; i++) {
                    int from = path[i];
                    int to  = path[i+1];
                    F[from][to]++;
                    F[to][from]--;
                }
            }else {
                for (int i = 0; i < N && !flowFound; i++) {
                    if (!visited[i] && A[u][i] > F[u][i]) {
                        visited[i] = true;
                        path[pathLen] = i;
                        pathLen++;
                        dfs(i);
                        visited[i] = false;
                        pathLen--;
                    }
                }
            }
        }
    }

    public static class Utilities{
        public static List<Integer> getPrimes(int limit) {
            boolean[] primes = new boolean[limit+1];
            Arrays.fill(primes, true);

            primes[1] = false;
            for(int i=2; i<=limit; i++){
                if (primes[i]){
                    for(int j=i+i; j<=limit; j+=i){
                        primes[j] = false;
                    }
                }
            }
            List<Integer> listPrimes = new ArrayList<>();
            for(int i=2; i<=limit; i++){
                if (primes[i]){
                    listPrimes.add(i);
                }
            }
            return listPrimes;
        }
    }

    public static class Modulo{
        long mod = (long)1e9+7;

        public Modulo(long mod) {
            super();
            this.mod = mod;
        }

        public long inv(long a) {
            long res =  pow(a, mod-2);
            return res;
        }

        public long pow(long a, long x) {
            if (x==0)
                return 1;
            long part = 1;
            if ((x&1)!=0)
                part = a;
            return (part * pow((a*a)%mod, x>>1)) % mod;
        }

        public long c(long n, long m){
            long res = 1;
            for(int i=1; i<=m; i++){
                res = (res * (n-m+i)) % mod;
                res = (res * inv(i)) % mod;
            }
            return res;
        }
    }

    /**
     * Added 26.04.2013.
     * See KROK 2013, Round 1, Problem D.
     */
    static class DisjointUnionSet implements Cloneable{
        int[] rank;
        int[] parent;

        protected DisjointUnionSet clone(){
            DisjointUnionSet cloned = new DisjointUnionSet(parent.length);
            for(int i=0; i<parent.length; i++){
                cloned.parent[i] = parent[i];
                cloned.rank[i] = rank[i];
            }
            return cloned;
        }

        public DisjointUnionSet(int n) {
            rank = new int[n];
            parent = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
            }
        }

        @Override
        public String toString() {
            return "disj [parents=" + Arrays.toString(parent) + "]";
        }

        /**
         * Problem specific or general?
         * O(N * alpha)
         */
        public void union(DisjointUnionSet set2){
            for(int i=0; i<parent.length; i++){
                parent[find(i)] = parent[find(set2.find(i))];
            }
        }

        /**
         * @param index1 range 0..n-1
         * @param index2
         */
        public void union(int index1, int index2){
            int p1 = find(index1);
            int p2 = find(index2);
            if (rank[p1] > rank[p2]){
                parent[p2] = p1;
            }else if (rank[p2] > rank[p1]){
                parent[p1] = p2;
            }else{
                parent[p2] = p1;
                rank[p1]++;
            }
        }

        // O(alpha(n))
        private int find(int index) {
            if (parent[index] != index)
                parent[index] =  find(parent[index]);
            return parent[index];
        }

        // O(N alpha(N)) ==> see find()
        public int getCountDisjointSets(){
            int[] used = new int[parent.length];
            for(int i=0; i<parent.length; i++){
                used[find(i)] = 1;
            }
            int res = 0;
            for(int i=0; i<parent.length; i++){
                res += used[i];
            }
            return res;
        }
    }

    private static Random rnd = new Random();
    public static class ArrayUtils{
        public static void shuffle(int[] a){
            for(int j=a.length-1; j>=1; j--){
                int i = rnd.nextInt(j+1);
                swap(a, i, j);
            }
        }

        public static void swap(int[] a, int i, int j){
            int tmp = a[i];
            a[i] = a[j];
            a[j] = tmp;
        }
    }

    static class GraphSupport{
        /*
        //Added 20.02.2017.
        //See Codeforces Round 398, Div.2, C.
        // Recoursive call to dfs function may result in either MTL or StackOverflow.
        // Codeforces provide stacksize 64M
 
        private void dfs_no_recursion(int root, IntConsumer dfs_post){
            int[] stack = new int[N];
            int[] stackInt = new int[N];
            int iStack = 0;
            stack[iStack] = root;
            stackInt[iStack++] = 0;
            while(true){
                Node node = nodes[stack[iStack-1]];
                int childIdx = stackInt[iStack-1];
                if (childIdx < node.children.size()){
                    stack[iStack] = node.children.get(childIdx).idx;
                    stackInt[iStack++] = 0;
                }else{
                    dfs_post.accept(node.idx);
 
                    iStack--;
                    if (iStack==0){
                        break;
                    }
                    stackInt[iStack-1]++;
                }
            }
        }
        */
    }


    ////////////////////////////////////////////////////////
    /// Typically, you don't want to edit anything below
    ///////////////////////////////////////////////////////
    final int BUF_SIZE = 1024 * 1024 * 8;//important to read long-string tokens properly
    final int INPUT_BUFFER_SIZE = 1024 * 1024 * 8;
    final int BUF_SIZE_INPUT = 1024;

    boolean useClassResourceTopDir = true;
    String outSuffix = ".out";

    static PrintStream outGlobal;
    static ByteScanner scanner;

    public void run() {
        try{
            InputStream bis;
            OutputStream bos;
            if (inputFilename !=null){
                File inputFile;
                File outputFile;
                if (useClassResourceTopDir) {
                    File baseFile = new File(getClass().getResource("/").getFile());
                    inputFile = new File(baseFile, inputFilename);
                    outputFile = new File(baseFile, inputFilename +outSuffix);
                }else{
                    inputFile = new File(inputFilename);
                    outputFile = new File(inputFilename +outSuffix);
                }
                System.out.println("Input file canonical path: "+inputFile.getCanonicalPath());
                bis = new BufferedInputStream(
                        new FileInputStream(inputFile),
                        INPUT_BUFFER_SIZE);
                bos = new BufferedOutputStream(new FileOutputStream(outputFile));
                outGlobal = new PrintStream(bos);
            }else{
                bis = new BufferedInputStream(System.in, INPUT_BUFFER_SIZE);
                bos = new BufferedOutputStream(System.out);
                outGlobal = new PrintStream(bos);
            }
            scanner = new ByteScanner(bis, BUF_SIZE_INPUT, BUF_SIZE);

            solveAll();
            outGlobal.flush();
        }catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    public static class EofException extends IOException{
    }

    public static class ByteScanner{
        InputStream is;

        public ByteScanner(InputStream is, int bufSizeInput, int bufSize){
            this.is = is;
            this.bufSizeInput = bufSizeInput;
            this.bufSize = bufSize;

            byteBufInput = new byte[this.bufSizeInput];
            byteBuf = new byte[this.bufSize];
        }

        public ByteScanner(byte[] data){
            byteBufInput = data;
            bufSizeInput = data.length;
            bufSize = data.length;
            byteBuf = new byte[bufSize];
            byteRead = data.length;
            bytePos = 0;
        }

        private int bufSizeInput;
        private int bufSize;

        byte[] byteBufInput;
        byte by=-1;
        int byteRead=-1;
        int bytePos=-1;

        byte[] byteBuf;
        int totalBytes;

        boolean eofMet = false;

        private byte nextByte() throws IOException{
            if (bytePos<0 || bytePos>=byteRead){
                byteRead = is==null? -1: is.read(byteBufInput);
                bytePos=0;
                if (byteRead<0){
                    byteBufInput[bytePos]=-1;//!!!
                    if (eofMet)
                        throw new EofException();
                    eofMet = true;
                }
            }
            return byteBufInput[bytePos++];
        }

        public byte nextVisibleChar() throws IOException{
            while ((by=nextByte())<=0x20);
            return by;
        }

        public String nextLine() throws IOException {
            readToken((byte)0x20);
            return new String(byteBuf,0,totalBytes);
        }

        // Reads token. Spacebar is separator char.
        public String nextToken() throws IOException {
            readToken((byte)0x21);
            return new String(byteBuf,0,totalBytes);
        }

        // Spacebar is included as separator char
        private void readToken() throws IOException {
            readToken((byte)0x21);
        }

        private void readToken(byte acceptFrom) throws IOException {
            totalBytes = 0;
            while ((by=nextByte())<acceptFrom);
            byteBuf[totalBytes++] = by;
            while ((by=nextByte())>=acceptFrom){
                byteBuf[totalBytes++] = by;
            }
        }

        public int nextInt() throws IOException{
            readToken();
            int num=0, i=0;
            boolean sign=false;
            if (byteBuf[i]=='-'){
                sign = true;
                i++;
            }
            for (; i<totalBytes; i++){
                num*=10;
                num+=byteBuf[i]-'0';
            }
            return sign?-num:num;
        }

        public long nextLong() throws IOException{
            readToken();
            long num=0;
            int i=0;
            boolean sign=false;
            if (byteBuf[i]=='-'){
                sign = true;
                i++;
            }
            for (; i<totalBytes; i++){
                num*=10;
                num+=byteBuf[i]-'0';
            }
            return sign?-num:num;
        }

        public double nextDouble() throws IOException{
            readToken();
            char[] token = new char[totalBytes];
            for (int i = 0; i < totalBytes; i++) {
                token[i] = (char)byteBuf[i];
            }
            return Double.parseDouble(new String(token));
        }

        public int[] loadIntArray(int size) throws IOException{
            int[] a = new int[size];
            for (int i = 0; i < a.length; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public long[] loadLongArray(int size) throws IOException{
            long[] a = new long[size];
            for (int i = 0; i < a.length; i++) {
                a[i] = nextLong();
            }
            return a;
        }
    }

    public static void main(String[] args) {
        new Main().run();
    }
}