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.DataInputStream;
import java.io.IOException;
import java.util.Scanner;

import static java.lang.System.*;

public class Main {

    private int n, m, k;

    private int gcd(int x, int y) {
        if (x == 0)
            return y;
        return this.gcd(y % x, x);
    }

    public void readData() throws IOException {
        Scanner input = new Scanner(in);

        n = input.nextInt();
        m = input.nextInt();
        k = input.nextInt();
    }

    public void SolveProblem() {
        int codiv_n_k = gcd(n, k);
        int codiv_m_k = gcd(m, k);

        if (codiv_n_k * 1L * codiv_m_k * 2 % k == 0) {
            out.println("YES");
            out.println("0 0");
            if (k / codiv_m_k == codiv_n_k * 2) {
                codiv_m_k *= 2;
                codiv_n_k *= 2;
            } else if (codiv_m_k > codiv_n_k) {
                codiv_n_k = k / codiv_m_k * 2;
            } else {
                codiv_m_k = k / codiv_n_k * 2;
            }
            out.println("0 " + m * 2 / codiv_m_k);
            out.println("" + n * 2 / codiv_n_k + " 0");
        } else {
            out.println("NO");
        }
    }

    public static void main(String[] args) throws  IOException {
        Main helper = new Main();
        helper.readData();
        helper.SolveProblem();
    }
}