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) {
        // TODO Auto-generated method stub
        Scanner in = new Scanner(System.in);
        long n = in.nextLong(), m = in.nextLong(), k = in.nextLong();

        if (n * m * 2 % k != 0)
            System.out.println("NO");
        else {
            System.out.println("YES");
            System.out.println("0 0");
            long u = gy(2 * n, k);
            long a = (long) 2 * n * m / k;
            if (u == 1) {
                System.out.println("0 " + 2 * m / k);
                System.out.println(n + " 0");
            } else {
                System.out.println("0 " + u * m / k);
                System.out.println(2 * n / u + " 0");
            }
        }
    }

    public static long gy(long a, long b) {
        while (b != 0) {
            long r = a % b;
            a = b;
            b = r;
        }
        return a;
    }

}

	         		    				   		 					