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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Solution {
    public static long gcd(long a, long b) {
        return b > 0 ? gcd(b, a % b) : a;
    }


    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String[] s = reader.readLine().split("\\s+");
        long n = Integer.parseInt(s[0]);
        long m = Integer.parseInt(s[1]);
        long k = Integer.parseInt(s[2]);

        long g = gcd(n * m, k);
        long x = gcd(n, k);
        long y = gcd(m, k);

        if (k != g && k != g * 2) {
            System.out.println("NO");
        } else {
            System.out.println("YES");
            if (x > 1) {
                long a2 = n / x;
                long a1 = k / x;
                y = gcd(a1, m);
                long a4 = m / y;
                if (k == g) {
                    System.out.println("0 0");
                    System.out.println("0 " + a4);
                    System.out.println(2*a2 + " 0");
                } else {
                    System.out.println("0 0");
                    System.out.println("0 " + a4);
                    System.out.println(a2 + " 0");
                }
            } else {
                x = gcd(m, k);
                long a2 = m / x;
                long a1 = k / x;
                y = gcd(a1, n);
                long a4 = n / y;
                if (k == g) {
                    System.out.println("0 0");
                    System.out.println("0 " + 2*a2);
                    System.out.println(a4 + " 0");
                } else {
                    System.out.println("0 0");
                    System.out.println("0 " + a2);
                    System.out.println(a4 + " 0");
                }
            }
        }

    }
}
