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.*;
import java.io.*;
import java.awt.Point;
import java.math.BigDecimal;
import java.math.BigInteger;

import static java.lang.Math.*;

// Solution is at the bottom of code

public class B implements Runnable{
	
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	
	BufferedReader in;
	OutputWriter out;
	StringTokenizer tok = new StringTokenizer("");
	
	public static void main(String[] args){
		new Thread(null, new B(), "", 128 * (1L << 20)).start();
	}
	
	/////////////////////////////////////////////////////////////////////
	
	void init() throws FileNotFoundException{
		Locale.setDefault(Locale.US);
		
		if (ONLINE_JUDGE){
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new OutputWriter(System.out);
		}else{
			in = new BufferedReader(new FileReader("input.txt"));
			out = new OutputWriter("output.txt");
		}
	}
	
	////////////////////////////////////////////////////////////////
	
	long timeBegin, timeEnd;

	void time(){
		timeEnd = System.currentTimeMillis();
		System.err.println("Time = " + (timeEnd - timeBegin));
	}
	
	void debug(Object... objects){
		if (ONLINE_JUDGE){
			for (Object o: objects){
				System.err.println(o.toString());
			}
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	public void run(){
		try{
			timeBegin = System.currentTimeMillis();
			Locale.setDefault(Locale.US);
			
			init();
			solve();
			
			out.close();
			time();
		}catch (Exception e){
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	String delim = " ";
	
	String readString() throws IOException{
		while(!tok.hasMoreTokens()){
			try{
				tok = new StringTokenizer(in.readLine());
			}catch (Exception e){
				return null;
			}
		}
		
		return tok.nextToken(delim);
	}
	
	String readLine() throws IOException{
		return in.readLine();
	}
	
	/////////////////////////////////////////////////////////////////
	
	final char NOT_A_SYMBOL = '\0';
	
	char readChar() throws IOException{
		int intValue = in.read();
		
		if (intValue == -1){
			return NOT_A_SYMBOL;
		}
		
		return (char) intValue;
	}
	
	char[] readCharArray() throws IOException{
		return readLine().toCharArray();
	}
	
	/////////////////////////////////////////////////////////////////
	
	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}
	
	int[] readIntArray(int size) throws IOException {
		int[] array = new int[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readInt();
		}
		
		return array;
	}
	
	int[] readIntArrayWithDecrease(int size) throws IOException {
		int[] array = readIntArray(size);
		
		for (int i = 0; i < size; ++i) {
			array[i]--;
		}
		
		return array;
	}
	
	///////////////////////////////////////////////////////////////////
	
	long readLong() throws IOException{
		return Long.parseLong(readString());
	}
	
	long[] readLongArray(int size) throws IOException{
		long[] array = new long[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readLong();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
	
	double readDouble() throws IOException{
		return Double.parseDouble(readString());
	}
	
	double[] readDoubleArray(int size) throws IOException{
		double[] array = new double[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readDouble();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
		
	BigInteger readBigInteger() throws IOException {
		return new BigInteger(readString());
	}
	
	BigDecimal readBigDecimal() throws IOException {
		return new BigDecimal(readString());
	}
	
	/////////////////////////////////////////////////////////////////////
	
	Point readPoint() throws IOException{
		int x = readInt();
		int y = readInt();
		return new Point(x, y);
	}
	
	Point[] readPointArray(int size) throws IOException{
		Point[] array = new Point[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readPoint();
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	List<Integer>[] readGraph(int vertexNumber, int edgeNumber)
	throws IOException{
		@SuppressWarnings("unchecked")
		List<Integer>[] graph = new List[vertexNumber];
		
		for (int index = 0; index < vertexNumber; ++index){
			graph[index] = new ArrayList<Integer>();
		}
		
		while (edgeNumber-- > 0){
			int from = readInt() - 1;
			int to = readInt() - 1;
			
			graph[from].add(to);
			graph[to].add(from);
		}
		
		return graph;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static class IntIndexPair {
		
		static Comparator<IntIndexPair> increaseComparator = new Comparator<B.IntIndexPair>() {
			
			@Override
			public int compare(IntIndexPair indexPair1, IntIndexPair indexPair2) {
				int value1 = indexPair1.value;
				int value2 = indexPair2.value;
				
				if (value1 != value2) return value1 - value2;
				
				int index1 = indexPair1.index;
				int index2 = indexPair2.index;
				
				return index1 - index2;
			}
		};
		
		static Comparator<IntIndexPair> decreaseComparator = new Comparator<B.IntIndexPair>() {
			
			@Override
			public int compare(IntIndexPair indexPair1, IntIndexPair indexPair2) {
				int value1 = indexPair1.value;
				int value2 = indexPair2.value;
				
				if (value1 != value2) return -(value1 - value2);
				
				int index1 = indexPair1.index;
				int index2 = indexPair2.index;
				
				return index1 - index2;
			}
		};
		
		int value, index;

		public IntIndexPair(int value, int index) {
			super();
			this.value = value;
			this.index = index;
		}		
		
		public int getRealIndex() {
			return index + 1;
		}
	}
	
	IntIndexPair[] readIntIndexArray(int size) throws IOException {
		IntIndexPair[] array = new IntIndexPair[size];
		
		for (int index = 0; index < size; ++index) {
			array[index] = new IntIndexPair(readInt(), index);
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static class OutputWriter extends PrintWriter{

		final int DEFAULT_PRECISION = 12;
		
		int precision;
		String format, formatWithSpace;
		
		{
			precision = DEFAULT_PRECISION;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		public OutputWriter(OutputStream out) {
			super(out);
		}

		public OutputWriter(String fileName) throws FileNotFoundException {
			super(fileName);
		}
		
		public int getPrecision() {
			return precision;
		}

		public void setPrecision(int precision) {
			precision = max(0, precision);
			this.precision = precision;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		private String createFormat(int precision){
			return "%." + precision + "f";
		}
		
		@Override
		public void print(double d){
			printf(format, d);
		}
		
		public void printWithSpace(double d){
			printf(formatWithSpace, d);
		}

		public void printAll(double...d){
			for (int i = 0; i < d.length - 1; ++i){
				printWithSpace(d[i]);
			}
			
			print(d[d.length - 1]);
		}
		
		@Override
		public void println(double d){
			printlnAll(d);
		}
		
		public void printlnAll(double... d){
			printAll(d);
			println();
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}}; 
	int[][] steps8 = {
			{-1, 0}, {1, 0}, {0, -1}, {0, 1},
			{-1, -1}, {1, 1}, {1, -1}, {-1, 1}
	};
	
	boolean check(int index, int lim){
		return (0 <= index && index < lim);
	}
	
	/////////////////////////////////////////////////////////////////////
	
	boolean checkBit(int mask, int bit){
		return (mask & (1 << bit)) != 0;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	long readLongFromDouble(int afterDotLength) throws IOException {
		String value = readString();
		int dotIndex = value.indexOf('.');
		
		long beforeDotPart = Long.parseLong(dotIndex == -1? value: value.substring(0, dotIndex));
		for (int i = 0; i < afterDotLength; ++i) {
			beforeDotPart *= 10;
		}
		
		long afterDotPart = (dotIndex == -1? 0: Long.parseLong(value.substring(dotIndex + 1)));
		for (int i = afterDotLength; i > value.length() - dotIndex - 1; --i) {
			afterDotPart *= 10;
		}
		
		return beforeDotPart + afterDotPart;
	}
	
	void solve() throws IOException {
		long squareSide = readLongFromDouble(4);
		long foodDistance = readLongFromDouble(4);
		
		int foodCount = readInt();
		
		final int[][] xCoefficients = {
				{0, 1},
				{1, 0},
				{1, -1},
				{0, 0}
		};
		
		final int[][] yCoefficients = {
				{0, 0},
				{0, 1}, 
				{1, 0},
				{1, -1}
		};
		
		long currentFoodDistance = foodDistance;
		while (foodCount --> 0) {
			long sideNumber = currentFoodDistance / squareSide;
			long afterCornerDistance = currentFoodDistance - squareSide * sideNumber;
			int sideIndex = (int) (sideNumber & 3);
			
			long currentX = squareSide * xCoefficients[sideIndex][0] + afterCornerDistance * xCoefficients[sideIndex][1];
			long currentY = squareSide * yCoefficients[sideIndex][0] + afterCornerDistance * yCoefficients[sideIndex][1];
			
			printLongAsDouble(currentX, 4);
			out.print(" ");
			printLongAsDouble(currentY, 4);
			out.println();
			
			currentFoodDistance += foodDistance;
		}
	}
	
	void printLongAsDouble(long value, int afterDotPart) {
		String stringValue = Long.toString(value);
		while (stringValue.length() <= afterDotPart) {
			stringValue = "0" + stringValue;
		}
		
		out.print(stringValue.substring(0, stringValue.length() - afterDotPart) + "." + stringValue.substring(stringValue.length() - afterDotPart));
	}
}