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.util.*;

public class Main {
    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        long n = in.nextLong();
        long m = in.nextLong();
        long k = in.nextLong();
        if(m == 0 || n == 0) {
            System.out.println("YES");
            System.out.print("0 0\n0 0\n0 0");
        }
        if((2 * n * m) % k == 0) {
            System.out.println("YES");
            long h, a, r, f, x;
            if((n * m) % k == 0) {
                r = gct(n, k);
                a = n / r;
                f = k / r;
                h = m / f;
                if(a * 2 <= n)
                    a *= 2;
                else
                    h *= 2;
            }
            else {
                r = gct(n, k);
                a = n / r;
                f = (k / r) / 2;
                h = m / f;
            }
            System.out.print("0 0\n0 " + h + "\n" + a + " 0");
        }
        else
            System.out.println("NO");
    }

    public static long gct(long a, long b) {
        long c;
        if(a < b)
        {
            c = a;
            a = b;
            b = c;
        }
        while (true){
            c = a % b;
            if(c == 0)
                return b;
            a = b;
            b = c;
        }
    }
}
