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 scanner = new Scanner(System.in);

        long n = scanner.nextLong();
        long m = scanner.nextLong();
        long k = scanner.nextLong();
        long j = 0;
        for (int i = 1; i * i <= k; i++) {
            if (k % i == 0) {
                j = k / i;
            }
            if (2 * m % i == 0) {
                if (n % j == 0 && i != 1) {
                    System.out.println("YES");
                    System.out.println("0 " + (2 * m / i));
                    System.out.println(0 + " 0");
                    System.out.println(n / j + " 0");
                    return;
                }
            }
            if (2 * n % i == 0) {
                if (m % j == 0 && i != 1) {
                    System.out.println("YES");
                    System.out.println(2 * n / i + " 0");
                    System.out.println(0 + " 0");
                    System.out.println("0 " + (m / j));
                    return;
                }
            }
            if (2 * m % j == 0) {
                if (n % i == 0 && j != 1) {
                    System.out.println("YES");
                    System.out.println(n / i + " 0");
                    System.out.println(0 + " 0");
                    System.out.println("0 " + (2 * m / j));
                    return;
                }
            }
            if (2 * n % j == 0) {
                if (m % i == 0 && j != 1) {
                    System.out.println("YES");
                    System.out.println(2 * n / j + " 0");
                    System.out.println(0 + " 0");
                    System.out.println("0 " + (m / i));
                    return;
                }

            }
        }
        System.out.println("NO");
    }
}
