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 A {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long n = scanner.nextInt();
        long m = scanner.nextInt();
        long k = scanner.nextInt();
        if (n * m * 2 % k != 0) {
            System.out.println("NO");
            return;
        }
        long t = k;
        boolean flag = false;
        boolean flag1 = false;
        if (t % 2 == 0) {
            t /= 2;
            flag1 = true;
        }
        for (long i = 2; i <= t; i++)
            while (t % i == 0) {
                t /= i;
                if (n % i == 0) {
                    n = n / i;
                    flag = true;
                } else if (m % i == 0) {
                    m = m / i;
                }
            }
        System.out.println("YES");
        System.out.println("0 0");
        if (flag1 == false) {
            if (flag) n = n * 2;
            else m = m * 2;
        }
        System.out.println(n + " 0");
        System.out.println("0 " + m);
    }

}
