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.Scanner;

public class Submission {
	
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scan = new Scanner(System.in);
		long n = scan.nextInt();
		long m = scan.nextInt();
		long k = scan.nextInt();
		boolean flag = false;//if not divide 2
		if((m*n%k != 0) 
				&& (2*(m*n%k) != k)){
			System.out.println("NO");
			scan.close();
			return;
		}
		System.out.println("YES");
		System.out.println("0 0");
		Submission sub = new Submission();
		if(k%2 == 0){
			k /= 2;
			flag = true;
		}
		long i = sub.gcd(n,k);
		k /= i;
		long j = sub.gcd(m, k);
		if(flag){
			System.out.println("0 " + m/j);
			System.out.println(n/i + " 0");
		}else{
			if(j < 2){
				System.out.println("0 " + m/j);
				System.out.println(2*n/i + " 0");
			}else{
				System.out.println("0 " + 2*m/j);
				System.out.println(n/i + " 0");
			}			
		}		
		scan.close();		
	}
	
	long gcd(long n,long m){
		while(m != 0){
			long r = n % m;
			n = m;
			m = r;
		}
		return n;
	}	
}