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 Solution {
	public static long getGcd(long x, long y)
	{
		if (x % y == 0)
			return y;
		return getGcd(y, x % y);
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		long m = sc.nextLong();
		long k = sc.nextLong();
		boolean result = false;

		long t = n * m * 2;
		if (t % k == 0)
		{
			t /= k;

			// Find a rectangle with area t/k
			long x = getGcd(t, n);
			long y = getGcd(t, m);
			if (x * y < t)
			{
				if (t / x <= m)
					y = t / x;
				else if (t / y <= n)
					x = t / y;
			}
			else if (x * y > t)
			{
				y = t / x;
			}

			System.out.println("YES");
			System.out.println("0 0");
			System.out.println(String.format("0 %d", y));
			System.out.print(String.format("%d 0", x));
			result = true;
		}

		if (!result)
			System.out.print("NO");
		sc.close();
	}

}
