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.math.*;
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();
        
        int flag = 1;
        if((2*n*m)%k != 0) flag = 0;
        
    	long area = 2*n*m/k;
    	long x = 2*n/gcd(2*n,k);
    	long y = area/x;
    	if(x > n){
    		x>>=1;
    		y<<=1;
    	}
    	if(flag == 1)
    	{
    		System.out.println("YES");
    		System.out.println(x+" 0");
    		System.out.println("0 0");
    		System.out.println("0 "+y);
    	}
    	else
    		System.out.println("NO");
    }
    
    public static long gcd(long a, long b){
    	if(b > 0) return gcd(b,a%b);
    	return a;
    }
}
    	    	 			 	 			 		  	   	