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:
/**
 * Author   : KillerCage
 * Language : Java
 * Time     : 2014 / 09
 * Quote    : E'la nostra ora incisa sull'anello
 */

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

public class Main {
	public static void main( String[] args ) throws IOException {
		InputStream is = System.in;
		OutputStream os = System.out;
		InputReader inr = new InputReader( is );
		PrintWriter out = new PrintWriter( os );

		Task KillerCage = new Task();
		KillerCage.solve( inr, out );

		out.close();
	}
}

/*__________________________iniz_of_task_____________________________________*/

class Task {
	InputReader inr;
	PrintWriter out;

	public void solve( InputReader inr, PrintWriter out ) {
		this.inr = inr; this.out = out;
		double a = inr.nextDouble(), d = inr.nextDouble();
		int n = inr.nextInt();
		for ( int i = 1; i <= n; i ++ ) {
			long s = ( long ) ( i * d / a / 4);
			double l = i * d - s * 4 * a;
			if ( l < a ) out.printf( "%.10f %.10f\n", l, 0.0 );
			else if ( l < a * 2 ) out.printf( "%.10f %.10f\n", a, l - a );
			else if ( l < a * 3 ) out.printf( "%.10f %.10f\n", 3 * a - l, a );
			else out.printf( "%.10f %.10f\n", 0.0, 4 * a - l );
		}
	}
}

/*__________________________fine_of_task_____________________________________*/

class InputReader {
	private InputStream is;
	int cur_byte_idx = 0;
	int bytes_in_buf = 0;
	byte buf[] = new byte[1024 << 4];

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

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

	public boolean isWhitespace( int c ) {
		return !( c >= 33 && c <= 126 );
	}

	public int skip() {
		int b;
		while ( ( b = readByte() ) != -1 && isWhitespace( b ) ) ;
		return b;
	}

	public Byte nextByte() {
		return ( byte ) skip();
	}

	public int nextInt() {
	// public long nextLong() {
		int b;
		while ( ( b = readByte() ) != -1 && 
			!( ( b >= '0' && b <= '9') || b == '-') );
		int symbol = 1;
		if ( b == '-' ) {
			b = readByte();
			symbol = -1;
		}
		int num = 0;
		// when nextLong: long num = 0;
		while ( true ) {
			if ( b >= '0' && b <= '9' ) {
				num = num * 10 + ( b - '0' );
			} else return symbol * num;
			b = readByte();
		}
	}

	public String next() {
	// public String nextLine() {
	int b = skip();
	StringBuilder sb = new StringBuilder();
	while ( !isWhitespace( b ) && true ) { // next
	// while ( !isWhitespace(b) || b == ' ') { // nextLine
		sb.appendCodePoint( b );
		b = readByte();
	}
	return sb.toString();
	}

	public byte[] next( int n ) {
	// public byte[] nextLine( int n ) {
		byte[] by = new byte[n];
		int b = skip(), len= 0;
		// while ( len < n && !isWhitespace( b ) ) {// next
		while ( len < n && ( !isWhitespace( b ) || b == ' ' ) ) {// nextLine
			by[len ++] = ( byte ) b;
			b = readByte();
		}
		if ( n == len ) return by;
		return Arrays.copyOf( by, len );
	}

	public double nextDouble() {
		return Double.parseDouble( next() );
	}
}