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.Arrays;
import java.util.Scanner;

public class Main 
{
	static long gcd(long a,long b)
	{
		if (b==0) return a;
		return gcd(b,a%b);
	}
	
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		long n,m,k;
		n = scanner.nextLong();
		m = scanner.nextLong();
		k = scanner.nextLong();
		scanner.close();
		if (n*m*2%k!=0)
		{
			System.out.print("NO\n");
			return;
		}
		System.out.print("YES\n0 0\n");
		long x= gcd(2*n,k),y;
		y=k/x;
		x=2*n/x;
		y=m/y;
		if (x<=n && y<=m)
		{
			System.out.format("%d %d\n",x,0);
			System.out.format("%d %d\n",0,y); 
		}else
		{
			x/=2;
			y*=2;
			System.out.format("%d %d\n",x,0);
			System.out.format("%d %d\n",0,y); 
		}
		
	}
	
}