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.
//package TCub2019Pass1;

import java.util.Scanner;

public class D {
    public static void main(String[] args) {
        final Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long m = sc.nextLong();
        long k = sc.nextLong();
        if (2 * m * n % k != 0)
            System.out.println("NO");
        else {
            boolean bm = true;
            if (k % 2 == 0) {
                k /= 2;
                bm = false;
            }

            final long g = gcd(k, n);
            long a = n / g, b = m * g / k;
            if (bm)
                if (g > 1)
                    a *= 2;
                else
                    b *= 2;
            System.out.printf("YES\n0 0\n%s 0\n0 %s", a, b);
        }
    }

    static long gcd(long a, long b){
        while (a > 0) {
            final long t = b % a;
            b = a;
            a = t;
        }

        return b;
    }
}
