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

public class triangle {

	public static void main(String[] args)throws IOException {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String[] inp= br.readLine().split(" ");
		double fn=Double.parseDouble(inp[0]);
		double fm=Double.parseDouble(inp[1]);
		double fk=Double.parseDouble(inp[2]);
		double n=fn,m=fm,k=fk;
		long x1=0,y1=0;
		int ch=0;
		for(int i=2;i<=fk;i++) {
			//System.out.println(i+" "+m+" "+m%i+" "+n%i );
			if(k%i==0 && n%i==0 && ch==0 ) {
				ch=1;
			}
			if(k%i==0 && m%i==0 && ch==0 ) {
				ch=2;
			}
			while(k%i==0 && n%i==0) {
				//System.out.println(n+" "+k);
				k=k/i;
				n=n/i;
			}
			while(k%i==0 && m%i==0) {
				//System.out.println(m+" "+k);
				k=k/i;
				m=m/i;
			}
			if(k<=2 || n*m*2<k)
				break;
		}
		if(k>2) {
			System.out.println("NO");
			return;
		}
		if(ch==1 && k<=2)
			n=n*(3-k);
		if(ch==2 && k<=2)
			m=m*(3-k);
		x1=(long)n;
		y1=(long)m;
		System.out.println("YES\n0 0\n0 "+y1+"\n"+x1+" 0");
	}
		
		
	
	
}
