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.*;

public class Main {

    public static void main(String[] args) {

        try (BufferedReader reader = new BufferedReader(new InputStreamReader(System.in))) {

            String[] line = reader.readLine().split(" ");
            long n = Long.parseLong(line[0]);
            long m = Long.parseLong(line[1]);
            long k = Long.parseLong(line[2]);
            boolean isEven = k % 2 == 0;
            if(isEven) {
                k /= 2;
            }

            boolean mb = true;

            if(n * m * 2 < k || n * m % k != 0) {
                println("NO");
            } else {
                long n_old = n;
                long test = nod(k, n);
                n /= test;
                k /= test;
                m /= nod(k, m);

                if(! isEven) {
                    if (n < n_old)
                        n *= 2;
                    else
                        m *= 2;
                }

                println("YES");
                println("0 0");
                println(n + " 0");
                println("0 " + m);
            }

        } catch (IOException e) {
        }
    }

    static long nod(long a, long b) {
        while(b != 0) {
            long c = a;
            a = b;
            b = c % b;
        }
        return a;
    }

    static int r(int a, int b) {
        int ans = a / b;
        if(a % b != 0) ans += 1;
        return ans;
    }

    static void print(Object c) {
        System.out.print(c.toString());
    }

    static void println(Object c) {
        System.out.println(c.toString());
    }
}