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.io.*;
import java.util.*;

import static java.lang.Math.*;

public class Main {

    public static double square(int x1, int y1, int x2, int y2, int x3, int y3) {
        return Math.abs((x1 - x3) * (y2 - y3) - (x2 - x3) * (y1 - y3)) / 2d;
    }

    public static void main(String[] args) throws IOException{
        Scanner scan = new Scanner(System.in);
        long n, m, k;
        n = scan.nextLong();
        m = scan.nextLong();
        k = scan.nextLong();
        long x1, x2, x3, y1, y2, y3;
        x1 = y1 = 0;
        x2 = y3 = 0;
        x3 = y2 = -1;
        if ((n * m * 2) % k != 0) {
            System.out.println("NO");
            return;
        }

        long square = (2 * n * m) / k;

        for (long i = max(min(square / n, square / m) - 1, 1); i <= max(square / m, square / n) + 1; i++) {
            if (square % i != 0) continue;
            if (square / i <= n && i <= m) {
               y2 = i;
               x3 = square / i;
               break;
            }
            if (square / i <= m && i <= n) {
                x3 = i;
                y2 = square / i;
                break;
            }
        }

        if (x3 == -1) {
            System.out.println("NO");
        } else {
            System.out.println("YES");
            System.out.println(x1 + " " + y1 +
                    "\n" + x3 + " " + y3 +
                    "\n" + x2 + " " + y2);
        }
    }
}