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.PrintWriter;
import java.util.Scanner;

import static java.lang.Integer.max;

/**
 * Created by Minology on 07:42 SA
 */
public class A {
    public static void main(String[] Args){
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        TaskA solver = new TaskA();
        solver.solve(in, out);
        out.close();
    }

    static class TaskA{
        public void solve(Scanner in, PrintWriter out){
            long n, m, k, a, b;
            n = in.nextInt();
            m = in.nextInt();
            k = in.nextInt();
            if (2 * n * m % k > 0){
                out.println("NO");
            }
            else{
                a = 2 * n; b = m;
                m = gcd(a, k); a /= m; k /= m;
                b /= k;
                if (a > n){
                    a /= 2;
                    b *= 2;
                }
                out.printf("YES\n%d 0\n0 %d\n0 0\n", a, b);
            }
        }

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