Vasya has got three integers n, m and k. He'd like to find three integer points (x_1, y_1), (x_2, y_2), (x_3, y_3), such that 0 ≤ x_1, x_2, x_3 ≤ n, 0 ≤ y_1, y_2, y_3 ≤ m and the area of the triangle formed by these points is equal to nm/k.

Help Vasya! Find such points (if it's possible). If there are multiple solutions, print any of them.

Input

The single line contains three integers n, m, k (1≤ n, m ≤ 10^9, 2 ≤ k ≤ 10^9).

Output

If there are no such points, print "NO".

Otherwise print "YES" in the first line. The next three lines should contain integers x_i, y_i — coordinates of the points, one point per line. If there are multiple solutions, print any of them.

You can print each letter in any case (upper or lower).

Examples

Input

4 3 3


Output

YES
1 0
2 3
4 1


Input

4 4 7


Output

NO

Note

In the first example area of the triangle should be equal to nm/k = 4. The triangle mentioned in the output is pictured below: 

<image>

In the second example there is no triangle with area nm/k = 16/7.
import javax.swing.plaf.basic.BasicInternalFrameTitlePane;
        import  java.io.*;
        import  java.math.*;
        import java.nio.Buffer;
        import java.sql.SQLSyntaxErrorException;
        import  java.util.*;
        import  java.text.*;
        import java.util.stream.Collectors;

public class Main {

    public static void main(String[] args) {
        Scanner cin = new Scanner(System.in);
        long n=cin.nextLong();
        long m=cin.nextLong();
        long k=cin.nextLong();
        if((n*m*2)%k!=0){
            System.out.println("NO");
            return;
        }
        long sum=n*m*2/k;
        long x1,y1,x2,y2,x3,y3;
        x1=y1=x2=y3=0;
        x3=y2=-1;
        long c1=Math.max(Math.min(sum/n,sum/m)-1,1);
        long c2=Math.max(sum/n,sum/m)+1;
        for(long i=c1;i<=c2;i++){
            if(sum%i!=0){
                continue;
            }
            if(sum/i<=n&&i<=m)
            {
                y2=i;
                x3=sum/i;
                break;
            }
            if(sum/i<=m&&i<=n){
                x3=i;
                y2=sum/i;
                break;
            }
        }
        if(x3==-1){
            System.out.println("NO");
        }
        else{
            System.out.println("YES");
            System.out.println(x1+" "+x2);
            System.out.println(x2+" "+y2);
            System.out.println(x3+" "+y3);
        }
        }

    }

 		      	    	 	   		   			