Problem: Valera takes part in the Berland Marathon. The marathon race starts at the stadium that can be represented on the plane as a square whose lower left corner is located at point with coordinates (0, 0) and the length of the side equals a meters. The sides of the square are parallel to coordinate axes.

As the length of the marathon race is very long, Valera needs to have extra drink during the race. The coach gives Valera a bottle of drink each d meters of the path. We know that Valera starts at the point with coordinates (0, 0) and runs counter-clockwise. That is, when Valera covers a meters, he reaches the point with coordinates (a, 0). We also know that the length of the marathon race equals nd + 0.5 meters. 

Help Valera's coach determine where he should be located to help Valera. Specifically, determine the coordinates of Valera's positions when he covers d, 2·d, ..., n·d meters.

Input

The first line contains two space-separated real numbers a and d (1 ≤ a, d ≤ 105), given with precision till 4 decimal digits after the decimal point. Number a denotes the length of the square's side that describes the stadium. Number d shows that after each d meters Valera gets an extra drink.

The second line contains integer n (1 ≤ n ≤ 105) showing that Valera needs an extra drink n times.

Output

Print n lines, each line should contain two real numbers xi and yi, separated by a space. Numbers xi and yi in the i-th line mean that Valera is at point with coordinates (xi, yi) after he covers i·d meters. Your solution will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Note, that this problem have huge amount of output data. Please, do not use cout stream for output in this problem.

Examples

Input

2 5
2


Output

1.0000000000 2.0000000000
2.0000000000 0.0000000000


Input

4.147 2.8819
6


Output

2.8819000000 0.0000000000
4.1470000000 1.6168000000
3.7953000000 4.1470000000
0.9134000000 4.1470000000
0.0000000000 2.1785000000
0.7034000000 0.0000000000

Solution (in JAVA):

Solution:
import java.util.NavigableSet;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.util.List;
import java.util.NoSuchElementException;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.Iterator;
import java.util.Collections;
import java.io.IOException;
import java.util.Arrays;
import java.util.TreeMap;
import java.io.InputStream;
import java.util.Random;
import java.util.Collection;
import java.util.Map;
import java.io.OutputStreamWriter;
import java.util.AbstractMap;
import java.util.Comparator;
import java.util.AbstractSet;
import java.util.SortedSet;
import java.util.Set;
import java.util.HashSet;
import java.util.TreeSet;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Árysson Cavalcanti
 */
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);
        TaskD2 solver = new TaskD2();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskD2 {

    int[] hx, hy, hl, vx, vy, vl;

    class Tree {
        Tree left, right;
        int value, middle, from, to;
        Tree(int from, int to) {
            this.from=from;
            this.to=to;
            middle=(from+to)/2;
            value=Integer.MIN_VALUE;
            if (from==to) return;
            left=new Tree(from, middle);
            right=new Tree(middle+1, to);
        }
        void update(int pos, int val) {
            if (from==to) {
                value=val;
                return;
            }
            if (pos<=middle) left.update(pos, val);
            else right.update(pos, val);
            value=MiscUtils.max(left.value, right.value);
        }
        int query(int from, int to) {
            if (to<this.from || from>this.to) return Integer.MIN_VALUE;
            if (from<=this.from && to>=this.to) return value;
            return MiscUtils.max(left.query(from, to), right.query(from, to));
        }
    }

    /*public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n=in.readInt(), m=in.readInt();
        hx=new int[n];
        hy=new int[n];
        hl=new int[n];
        vx=new int[m];
        vy=new int[m];
        vl=new int[m];
        IOUtils.readIntArrays(in, hx, hy, hl);
        IOUtils.readIntArrays(in, vx, vy, vl);
        out.printLine(MiscUtils.binarySearch(1, MiscUtils.max(ArrayUtils.maxElement(hl), ArrayUtils.maxElement(vl)), new Function<Long, Boolean>() {
            public Boolean value (Long size) {
                if (size==1) return true;
                boolean ret=true;
                CPPTreeMap<Integer, List<IntPair>> map=new CPPTreeMap<>(new Factory<List<IntPair>>() {
                    public List<IntPair> create() {
                        return new ArrayList<IntPair>();
                    }
                });
                List<Pair<IntPair, IntPair>> hor=new ArrayList<>(), ver=new ArrayList<>();
                TreapSet<Integer> set=new TreapSet<>();
                for (int i=0; i<n; i++) {
                    int x=hx[i], y1=hy[i]+(int)(long)size, y2=hy[i]+hl[i]-(int)(long)size;
                    if(y2>=y1){
                        ver.add(Pair.makePair(new IntPair(x, y1), new IntPair(x, y2)));
                        IntPair pair=new IntPair(1, ver.size()-1);
                        map.get(x).add(pair);
                        set.add(y1);
                        set.add(y2);
                    }
                }
                for (int i=0; i<m; i++) {
                    int x1=vx[i]+(int)(long)size, x2=vx[i]+vl[i]-(int)(long)size, y=vy[i];
                    if (x1<=x2) {
                        hor.add(Pair.makePair(new IntPair(x1, y), new IntPair(x2, y)));
                        IntPair pair=new IntPair(0, hor.size()-1);
                        map.get(x1).add(pair);
                        map.get(x2).add(pair);
                        set.add(y);
                    }
                }
                System.out.println(size);
                System.out.println(hor);
                System.out.println(ver);
                if (set.isEmpty()) return true;
                {
                    for (int i: set) System.out.print(i+" ");
                    System.out.println();
                }
                Indexer<Integer> indexer=new Indexer<>();
                for (int i: set) indexer.get(i);
                {
                    for (int i: indexer.keySet()) System.out.printf("(%d,%d) ", i, indexer.get(i));
                    System.out.println();
                }
                Tree tree=new Tree(0, indexer.size()-1);
                for (int x: map.keySet()) {
                    for (IntPair pair: map.get(x)) {
                        int t=pair.first, x1=hor.get(pair.second).first.first, x2=hor.get(pair.second).second.first, y1=hor.get(pair.second).first.second, y2=hor.get(pair.second).second.second;
                        if (t==0) {
                            if (x==x1) tree.update(indexer.get(y1), x2);
                        } else ret&=tree.query(indexer.get(y1), indexer.get(y2))<x;
                    }
                }
                for (int x: map.keySet()) {
                    for (IntPair pair: map.get(x)) {
                        int t=pair.first, x1=hor.get(pair.second).first.first, x2=hor.get(pair.second).second.first, y1=hor.get(pair.second).first.second, y2=hor.get(pair.second).second.second;
                        if (t==1 && x==x2) tree.update(indexer.get(y1), Integer.MIN_VALUE);
                    }
                }
                return ret;
            }
        })-1);
    }*/
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        double a=in.readDouble(), d=in.readDouble(), pos=0;
        int n=in.readInt();
        for (int i=1; i<=n; i++) {
            pos=(pos+d)%(4*a);
            //System.out.println(pos);
            if (pos<=a) System.out.println(pos+" "+0);
            else if (pos<=2*a) System.out.println(a+" "+(pos-a));
            else if (pos<=3*a) System.out.println((3*a-pos)+" "+a);
            else System.out.println(0+" "+(4*a-pos));
        }
    }
    
    List<IntPair> bfs(TreeSet<Integer>[] dist, int k, int n) {
        List<IntPair> ret=new ArrayList<IntPair>();
        int[] degree=new int[n+1];
        if (dist[0].size()!=1) return null;
        for (int i=1; i<n; i++) {
            for (Object J: dist[i].toArray()) {
                int j=(int)(Integer)J;
                if (dist[i-1].size()==0) return null;
                int x=dist[i-1].first();
                degree[j]++;
                degree[x]++;
                ret.add(new IntPair(j, x));
                if (degree[x]==k) dist[i-1].remove(x);
                if (degree[j]==k) dist[i].remove(j);
            }
        }
        return ret;
    }
}

class MiscUtils {

    public static long binarySearch(long from, long to, Function<Long, Boolean> function) {
        while (from < to) {
            long argument = from + (to - from) / 2;
            if (function.value(argument))
                to = argument;
            else
                from = argument + 1;
        }
        return from;
    }

    public static<T extends Comparable<T>> T max(T first, T second) {
        if (first.compareTo(second) <= 0)
            return second;
        return first;
    }

}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private 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 readInt() {
        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 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 interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
    
    public String readString() {
                int c = read();
                while (isSpaceChar(c))
                        c = read();
                StringBuilder res = new StringBuilder();
                do {
                        if (Character.isValidCodePoint(c))
                                res.appendCodePoint(c);
                        c = read();
                } while (!isSpaceChar(c));
                return res.toString();
   }
   
   public double readDouble() {
                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, readInt());
                        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, readInt());
                                if (c < '0' || c > '9')
                                        throw new InputMismatchException();
                                m /= 10;
                                res += (c - '0') * m;
                                c = read();
                        }
                }
                return res * sgn;
        }
        
}

class OutputWriter {
    private final PrintWriter writer;

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

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

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

}

class IOUtils {

    public static void readIntArrays(InputReader in, int[]... arrays) {
        for (int i = 0; i < arrays[0].length; i++) {
            for (int j = 0; j < arrays.length; j++)
                arrays[j][i] = in.readInt();
        }
    }

}

interface Function<A, V> {
    public abstract V value(A argument);
}

class ArrayUtils {

    public static int maxElement(int[] array) {
        return maxElement(array, 0, array.length);
    }

    public static int maxElement(int[] array, int from, int to) {
        int result = Integer.MIN_VALUE;
        for (int i = from; i < to; i++)
            result = Math.max(result, array[i]);
        return result;
    }

}

class CPPTreeMap<K, V> extends TreeMap<K, V> {
    private final Factory<V> defaultValueFactory;

    public CPPTreeMap(Factory<V> defaultValueFactory) {
        this.defaultValueFactory = defaultValueFactory;
    }

    public V get(Object key) {
        if (containsKey(key))
            return super.get(key);
        V value = defaultValueFactory.create();
        try {
            //noinspection unchecked
            super.put((K) key, value);
            return value;
        } catch (ClassCastException e) {
            return value;
        }
    }
}

class IntPair implements Comparable<IntPair> {
    public final int first, second;

    public IntPair(int first, int second) {
        this.first = first;
        this.second = second;
    }

    public String toString() {
        return "(" + first + "," + second + ")";
    }

    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        IntPair intPair = (IntPair) o;

        return first == intPair.first && second == intPair.second;

    }

    public int hashCode() {
        int result = first;
        result = 31 * result + second;
        return result;
    }

    public int compareTo(IntPair o) {
        if (first < o.first)
            return -1;
        if (first > o.first)
            return 1;
        if (second < o.second)
            return -1;
        if (second > o.second)
            return 1;
        return 0;
    }
}

interface Factory<V> {
    public V create();
}

class Pair<U, V> implements Comparable<Pair<U, V>> {
    public final U first;
    public final V second;

    public static<U, V> Pair<U, V> makePair(U first, V second) {
        return new Pair<U, V>(first, second);
    }

    private Pair(U first, V second) {
        this.first = first;
        this.second = second;
    }

    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Pair pair = (Pair) o;

        return !(first != null ? !first.equals(pair.first) : pair.first != null) && !(second != null ? !second.equals(pair.second) : pair.second != null);

    }

    public int hashCode() {
        int result = first != null ? first.hashCode() : 0;
        result = 31 * result + (second != null ? second.hashCode() : 0);
        return result;
    }

    public String toString() {
        return "(" + first + "," + second + ")";
    }

    public int compareTo(Pair<U, V> o) {
        int value = ((Comparable<U>)first).compareTo(o.first);
        if (value != 0)
            return value;
        return ((Comparable<V>)second).compareTo(o.second);
    }
}

class TreapSet<K> implements NavigableSet<K> {
    protected static final Random rnd = new Random(239);

    protected final Node nullNode;
    protected final Comparator<? super K> comparator;
    protected Node root;
    private final K from;
    private final K to;
    private final boolean fromInclusive;
    private final boolean toInclusive;

    public TreapSet() {
        this((Comparator<? super K>)null);
    }

    public TreapSet(Comparator<? super K> comparator) {
        this(null, null, false, false, comparator, null, null);
    }

    protected TreapSet(K from, K to, boolean fromInclusive, boolean toInclusive, Comparator<? super K> comparator, Node root, Node nullNode) {
        this.comparator = comparator;
        this.from = from;
        this.to = to;
        this.fromInclusive = fromInclusive;
        this.toInclusive = toInclusive;
        if (nullNode == null)
            nullNode = new NullNode();
        if (root == null)
            root = nullNode;
        this.root = root;
        this.nullNode = nullNode;
    }

    public boolean addAll(Iterable<? extends K> collection) {
        boolean result = false;
        for (K element : collection)
            result |= add(element);
        return result;
    }

    public K lower(K k) {
        Node target = root.lower(k);
        if (target == nullNode)
            return null;
        if (belongs(target.key))
            return target.key;
        return null;
    }

    private boolean belongs(K key) {
        int valueFrom = compare(from, key);
        int valueTo = compare(key, to);
        return (valueFrom < 0 || valueFrom == 0 && fromInclusive) && (valueTo < 0 || valueTo == 0 && toInclusive);
    }

    public K floor(K k) {
        Node target = root.floor(k);
        if (target == nullNode)
            return null;
        if (belongs(target.key))
            return target.key;
        return null;
    }

    public K ceiling(K k) {
        Node target = root.ceil(k);
        if (target == nullNode)
            return null;
        if (belongs(target.key))
            return target.key;
        return null;
    }

    public K higher(K k) {
        Node target = root.higher(k);
        if (target == nullNode)
            return null;
        if (belongs(target.key))
            return target.key;
        return null;
    }

    public K pollFirst() {
        K first = first();
        if (first == null)
            throw new NoSuchElementException();
        root.erase(first);
        return first;
    }

    public K pollLast() {
        K last = last();
        if (last == null)
            throw new NoSuchElementException();
        root.erase(last);
        return last;
    }

    public int size() {
        if (from == null && to == null)
            return root.size;
        if (from == null) {
            Node to = toInclusive ? root.floor(this.to) : root.lower(this.to);
            if (to == nullNode)
                return 0;
            return root.indexOf(to) + 1;
        }
        if (to == null) {
            Node from = fromInclusive ? root.ceil(this.from) : root.higher(this.from);
            if (from == nullNode)
                return 0;
            return root.size - root.indexOf(from);
        }
        Node from = fromInclusive ? root.ceil(this.from) : root.higher(this.from);
        if (from == nullNode || !belongs(from.key))
            return 0;
        Node to = toInclusive ? root.floor(this.to) : root.lower(this.to);
        return root.indexOf(to) - root.indexOf(from) + 1;
    }

    public boolean isEmpty() {
        return size() == 0;
    }

    public boolean contains(Object o) {
        return belongs((K) o) && root.search((K) o) != nullNode;
    }

    public Iterator<K> iterator() {
        return new Iterator<K>() {
            private K current = first();

            public boolean hasNext() {
                return current != null;
            }

            public K next() {
                K result = current;
                current = higher(current);
                return result;
            }

            public void remove() {
                TreapSet.this.remove(current);
            }
        };
    }

    public Object[] toArray() {
        Object[] array = new Object[size()];
        int index = 0;
        for (K key : this)
            array[index++] = key;
        return array;
    }

    public <T> T[] toArray(T[] a) {
        if (a.length < size())
            throw new IllegalArgumentException();
        int index = 0;
        for (K key : this)
            a[index++] = (T) key;
        return a;
    }

    public boolean add(K k) {
        if (k == null)
            throw new NullPointerException();
        if (contains(k))
            return false;
        root = root.insert(createNode(k));
        return true;
    }

    protected Node createNode(K k) {
        return new Node(k, rnd.nextLong());
    }

    public boolean remove(Object o) {
        if (!contains(o))
            return false;
        //noinspection unchecked
        root = root.erase((K) o);
        return true;
    }

    public boolean containsAll(Collection<?> c) {
        for (Object o : c) {
            if (!contains(o))
                return false;
        }
        return true;
    }

    public boolean addAll(Collection<? extends K> c) {
        return addAll((Iterable<? extends K>)c);
    }

    public boolean retainAll(Collection<?> c) {
        List<K> toRemove = new ArrayList<K>();
        for (K key : this) {
            if (!c.contains(key))
                toRemove.add(key);
        }
        return removeAll(toRemove);
    }

    public boolean removeAll(Collection<?> c) {
        boolean result = false;
        for (Object o : c)
            result |= remove(o);
        return result;
    }

    public void clear() {
        retainAll(Collections.<Object>emptySet());
    }

    public NavigableSet<K> descendingSet() {
        throw new UnsupportedOperationException();
    }

    public Iterator<K> descendingIterator() {
        return new Iterator<K>() {
            private K current = last();

            public boolean hasNext() {
                return current != null;
            }

            public K next() {
                K result = current;
                current = lower(current);
                return result;
            }

            public void remove() {
                TreapSet.this.remove(current);
            }
        };
    }

    public NavigableSet<K> subSet(K fromElement, boolean fromInclusive, K toElement, boolean toInclusive) {
        return new TreapSet<K>(fromElement, toElement, fromInclusive, toInclusive, comparator, root, nullNode);
    }

    public NavigableSet<K> headSet(K toElement, boolean inclusive) {
        return subSet(null, false, toElement, inclusive);
    }

    public NavigableSet<K> tailSet(K fromElement, boolean inclusive) {
        return subSet(fromElement, inclusive, null, false);
    }

    public Comparator<? super K> comparator() {
        return comparator;
    }

    public SortedSet<K> subSet(K fromElement, K toElement) {
        return subSet(fromElement, true, toElement, false);
    }

    public SortedSet<K> headSet(K toElement) {
        return subSet(null, false, toElement, false);
    }

    public SortedSet<K> tailSet(K fromElement) {
        return tailSet(fromElement, true);
    }

    public K first() {
        if (isEmpty())
            return null;
        if (from == null)
            return root.first().key;
        if (fromInclusive)
            return ceiling(from);
        return higher(from);
    }

    public K last() {
        if (isEmpty())
            return null;
        if (to == null)
            return root.last().key;
        if (toInclusive)
            return floor(to);
        return lower(to);
    }

    protected int compare(K first, K second) {
        if (first == null || second == null)
            return -1;
        if (comparator != null)
            return comparator.compare(first, second);
        //noinspection unchecked
        return ((Comparable<? super K>)first).compareTo(second);
    }

    protected class Node {
        protected final K key;
        protected final long priority;
        protected Node left;
        protected Node right;
        protected int size;

        protected Node(K key, long priority) {
            this.key = key;
            this.priority = priority;
            left = nullNode;
            right = nullNode;
            size = 1;
        }

        protected Object[] split(K key) {
            if (compare(key, this.key) < 0) {
                Object[] result = left.split(key);
                left = (Node) result[1];
                result[1] = this;
                updateSize();
                return result;
            }
            Object[] result = right.split(key);
            right = (Node) result[0];
            result[0] = this;
            updateSize();
            return result;
        }

        protected void updateSize() {
            size = left.size + right.size + 1;
        }

        protected Node insert(Node node) {
            if (node.priority > priority) {
                Object[] result = split(node.key);
                node.left = (Node) result[0];
                node.right = (Node) result[1];
                node.updateSize();
                return node;
            }
            if (compare(node.key, this.key) < 0) {
                left = left.insert(node);
                updateSize();
                return this;
            }
            right = right.insert(node);
            updateSize();
            return this;
        }

        protected Node merge(Node left, Node right) {
            if (left == nullNode)
                return right;
            if (right == nullNode)
                return left;
            if (left.priority > right.priority) {
                left.right = left.right.merge(left.right, right);
                left.updateSize();
                return left;
            }
            right.left = right.left.merge(left, right.left);
            right.updateSize();
            return right;
        }

        protected Node erase(K key) {
            int value = compare(key, this.key);
            if (value == 0)
                return merge(left, right);
            if (value < 0) {
                left = left.erase(key);
                updateSize();
                return this;
            }
            right = right.erase(key);
            updateSize();
            return this;
        }

        protected Node lower(K key) {
            if (compare(key, this.key) <= 0)
                return left.lower(key);
            Node result = right.lower(key);
            if (result == nullNode)
                return this;
            return result;
        }

        protected Node floor(K key) {
            if (compare(key, this.key) < 0)
                return left.floor(key);
            Node result = right.floor(key);
            if (result == nullNode)
                return this;
            return result;
        }

        protected Node higher(K key) {
            if (compare(key, this.key) >= 0)
                return right.higher(key);
            Node result = left.higher(key);
            if (result == nullNode)
                return this;
            return result;
        }

        protected Node ceil(K key) {
            if (compare(key, this.key) > 0)
                return right.ceil(key);
            Node result = left.ceil(key);
            if (result == nullNode)
                return this;
            return result;
        }

        protected Node first() {
            if (left == nullNode)
                return this;
            return left.first();
        }

        protected Node last() {
            if (right == nullNode)
                return this;
            return right.last();
        }

        protected Node search(K key) {
            int value = compare(key, this.key);
            if (value == 0)
                return this;
            if (value < 0)
                return left.search(key);
            return right.search(key);
        }

        public int indexOf(Node node) {
            if (this == node)
                return left.size;
            if (compare(node.key, this.key) > 0)
                return left.size + 1 + right.indexOf(node);
            return left.indexOf(node);
        }

    }

    private class NullNode extends Node {
        private Object[] splitResult = new Object[2];

        private NullNode() {
            super(null, Long.MIN_VALUE);
            left = this;
            right = this;
            size = 0;
        }

        protected Object[] split(K key) {
            splitResult[0] = splitResult[1] = this;
            return splitResult;
        }

        protected Node insert(Node node) {
            return node;
        }

        protected Node erase(K key) {
            return this;
        }

        protected Node lower(K key) {
            return this;
        }

        protected Node floor(K key) {
            return this;
        }

        protected Node higher(K key) {
            return this;
        }

        protected Node ceil(K key) {
            return this;
        }

        protected Node first() {
            throw new NoSuchElementException();
        }

        protected Node last() {
            throw new NoSuchElementException();
        }

        protected void updateSize() {
        }

        protected Node search(K key) {
            return this;
        }


    }
}

class Indexer<K> extends EHashMap<K, Integer> {
    private int index = 0;

    public Integer get(Object key) {
        if (!containsKey(key))
            put((K) key, index++);
        return super.get(key);
    }
}

class EHashMap<E, V> extends AbstractMap<E, V> {
    private static final int[] shifts = new int[10];

    private int size;
    private HashEntry<E, V>[] data;
    private int capacity;
    private Set<Entry<E, V>> entrySet;

    static {
        Random random = new Random(System.currentTimeMillis());
        for (int i = 0; i < 10; i++)
            shifts[i] = 1 + 3 * i + random.nextInt(3);
    }

    public EHashMap() {
        this(4);
    }

    private void setCapacity(int size) {
        capacity = Integer.highestOneBit(4 * size);
        //noinspection unchecked
        data = new HashEntry[capacity];
    }

    public EHashMap(int maxSize) {
        setCapacity(maxSize);
        entrySet = new AbstractSet<Entry<E, V>>() {
            public Iterator<Entry<E, V>> iterator() {
                return new Iterator<Entry<E, V>>() {
                    private HashEntry<E, V> last = null;
                    private HashEntry<E, V> current = null;
                    private HashEntry<E, V> base = null;
                    private int lastIndex = -1;
                    private int index = -1;

                    public boolean hasNext() {
                        if (current == null) {
                            for (index++; index < capacity; index++) {
                                if (data[index] != null) {
                                    base = current = data[index];
                                    break;
                                }
                            }
                        }
                        return current != null;
                    }

                    public Entry<E, V> next() {
                        if (!hasNext())
                            throw new NoSuchElementException();
                        last = current;
                        lastIndex = index;
                        current = current.next;
                        if (base.next != last)
                            base = base.next;
                        return last;
                    }

                    public void remove() {
                        if (last == null)
                            throw new IllegalStateException();
                        size--;
                        if (base == last)
                            data[lastIndex] = last.next;
                        else
                            base.next = last.next;
                    }
                };
            }

            public int size() {
                return size;
            }
        };
    }

    public Set<Entry<E, V>> entrySet() {
        return entrySet;
    }

    public void clear() {
        Arrays.fill(data, null);
        size = 0;
    }

    private int index(Object o) {
        return getHash(o.hashCode()) & (capacity - 1);
    }

    private int getHash(int h) {
        int result = h;
        for (int i : shifts)
            result ^= h >>> i;
        return result;
    }

    public V remove(Object o) {
        if (o == null)
            return null;
        int index = index(o);
        HashEntry<E, V> current = data[index];
        HashEntry<E, V> last = null;
        while (current != null) {
            if (current.key.equals(o)) {
                if (last == null)
                    data[index] = current.next;
                else
                    last.next = current.next;
                size--;
                return current.value;
            }
            last = current;
            current = current.next;
        }
        return null;
    }

    public V put(E e, V value) {
        if (e == null)
            return null;
        int index = index(e);
        HashEntry<E, V> current = data[index];
        if (current != null) {
            while (true) {
                if (current.key.equals(e)) {
                    V oldValue = current.value;
                    current.value = value;
                    return oldValue;
                }
                if (current.next == null)
                    break;
                current = current.next;
            }
        }
        if (current == null)
            data[index] = new HashEntry<E, V>(e, value);
        else
            current.next = new HashEntry<E, V>(e, value);
        size++;
        if (2 * size > capacity) {
            HashEntry<E, V>[] oldData = data;
            setCapacity(size);
            for (HashEntry<E, V> entry : oldData) {
                while (entry != null) {
                    HashEntry<E, V> next = entry.next;
                    index = index(entry.key);
                    entry.next = data[index];
                    data[index] = entry;
                    entry = next;
                }
            }
        }
        return null;
    }

    public V get(Object o) {
        if (o == null)
            return null;
        int index = index(o);
        HashEntry<E, V> current = data[index];
        while (current != null) {
            if (current.key.equals(o))
                return current.value;
            current = current.next;
        }
        return null;
    }

    public boolean containsKey(Object o) {
        if (o == null)
            return false;
        int index = index(o);
        HashEntry<E, V> current = data[index];
        while (current != null) {
            if (current.key.equals(o))
                return true;
            current = current.next;
        }
        return false;
    }

    public int size() {
        return size;
    }

    private static class HashEntry<E, V> implements Entry<E, V> {
        private final E key;
        private V value;
        private HashEntry<E, V> next;

        private HashEntry(E key, V value) {
            this.key = key;
            this.value = value;
        }


        public E getKey() {
            return key;
        }

        public V getValue() {
            return value;
        }

        public V setValue(V value) {
            V oldValue = this.value;
            this.value = value;
            return oldValue;
        }
    }
}