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(), m = scanner.nextLong(), k = scanner.nextLong();
        boolean isEven = k % 2 == 0;
        long p = n * m;
        if (isEven) k /= 2;

        if (p % k != 0) {
            System.out.println("NO");
            return;
        }
        long x = gcd(n, k);
        k /= x;
        long a = n / x;

        x = gcd(m, k);
        k /= x;
        assert (k == 1);
        long b = m / x;

        if (!isEven) {
            if (a < n)
                a += a;
            else {
                assert (b < m);
                b += b;
            }
        }

        System.out.println("YES");
        System.out.println("0 0");
        System.out.println(0 + " " + b);
        System.out.println(a + " " + 0);
    }

    /**
     * Нод
     */
    public static long gcd(long a, long b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

}