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.Scanner;

public class D {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long m = sc.nextLong();
        long k = sc.nextLong();
        if ((2 * n * m) % k != 0) {
            System.out.println("NO");
            return;
        }
        boolean mul = false;
        if (k % 2 == 0) {
            k /= 2;
            mul = true;
        }
        long g = gcd(k, n);
        long k1 = k / g;
        long a = n / g;
        long b = m / k1;
        if (!mul) {
            if (a < n) {
                a *= 2;
            } else {
                b *= 2;
            }
        }
        System.out.println("YES");
        System.out.println(0 + " " + 0);
        System.out.println(a + " " + 0);
        System.out.println(0 + " " + b);
    }

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