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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class CFTest123
{

	static BufferedReader br;

	public static void main(String[] args) {
		br = new BufferedReader(new InputStreamReader(System.in));

		try {

			double[]arr=readDoubleArr();
			
			double a=arr[0];
			double d=arr[1];
			int n=readInt();
			
			br.close();
			
			for(int i=1;i<=n;i++){
				double val=d*i;
				double div=val/a;
				long flr=(long)Math.floor(div);
				
				double ml=a*flr;
				double sb=val-ml;
				long md=flr%4;
				if(md==0){
					System.out.println(sb+" "+0);
				}else if(md==1){
					System.out.println(a+" "+sb);
				}else if(md==2){
					double dff=a-sb;
					System.out.println(dff+" "+a);
				}else{
					double dff=a-sb;
					System.out.println(0+" "+dff);
				}
			}
			
			
		} catch (IOException e) {
			e.printStackTrace();
		}

	}
	
	static String pro(int h1,int m1,int h2,int m2){
		int nhr=h1+h2;
		int nm=m1+m2;
		if(nm>59){
			nm-=60;
			nhr+=1;
		}
		String s=""+nhr;
		if(nhr<10)s="0"+s;
		String s2=""+nm;
		if(nm<10)s2="0"+s2;
		return s+":"+s2;
		
	}

	static public String readLine() throws IOException {
		return br.readLine();

	}

	static public String readString() throws IOException {
		return br.readLine();

	}

	static public long readlong() throws IOException {
		return Long.parseLong(br.readLine());
	}

	static public int readInt() throws IOException {
		return Integer.parseInt(br.readLine());
	}

	static public int[] readIntArr() throws IOException {
		String[] str = br.readLine().split(" ");
		int arr[] = new int[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = Integer.parseInt(str[i]);
		return arr;
	}

	static public double[] readDoubleArr() throws IOException {
		String[] str = br.readLine().split(" ");
		double arr[] = new double[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = Double.parseDouble(str[i]);
		return arr;
	}

	static public long[] readLongArr() throws IOException {
		String[] str = br.readLine().split(" ");
		long arr[] = new long[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = Long.parseLong(str[i]);
		return arr;
	}

	static public double readDouble() throws IOException {
		return Double.parseDouble(br.readLine());
	}
}