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 Main {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
        long n = sc.nextInt();
        long m = sc.nextInt();
        long k = sc.nextInt();
        long kk = k;
        if (2*m*n%k != 0) {
            System.out.println("NO");
            System.exit(0);
        }
        if (k%2 == 0) {
            k /= 2;
        }
        long ax, ay, bx, by, cx, cy;
        ax = 0;
        ay = 0;
        by = 0;
        cx = 0;
        //Will be changed
        bx = 0;
        cy = 0;
        long gcdN = gcd(n, k);
        //System.out.println(gcd);
        bx = n/gcdN;
        cy = (m*gcdN)/k;
        if (kk % 2 == 1) {
            if (bx < n) {
                bx *= 2;
            }
            else {
                cy *= 2;
            }
        }
        System.out.println("YES");
        System.out.printf("%d %d\n", ax, ay);
        System.out.printf("%d %d\n", bx, by);
        System.out.printf("%d %d\n", cx, cy);
        System.exit(0);
        
        
        
        
        
        sc.close();
    }
    
    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a%b);
    }
	

}
