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.
n, m, k = map(int, input().split())


def gcd(x, y):
    if y > 0:
        return gcd(y, x % y)
    else:
        return x


if m * n * 2 % k != 0:
    print("NO")
else:
    print("YES")
    a = m * n * 2 / k
    g = gcd(2 * n, k)
    if g != 1:
        x = 2 * n / g
        y = m * g / k
    else:
        x = n
        y = m * 2 / k
    print(0, 0)
    print(int(x), 0)
    print(0, int(y))

					  	 		 	 				 	   	 		 	 	