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 math

n, m, k = map(int, input().split())
x1 = 0
y1 = 0
x2 = 0
y2 = 0
x3 = 0
y3 = 0
if (2 * n * m) % k != 0:
    print("NO")
else:
    tmp = math.gcd(2 * n, k)
    if tmp > 1:
        x2 = 2 * n // tmp
        y3 = m * tmp // k
    else:
        tmp = math.gcd(2 * m, k)
        x2 = n * tmp // k
        y3 = 2 * m // tmp
    print("YES")
    print(x1, y1)
    print(x2, y2)
    print(x3, y3)

     	 		 		  	 	 	 					   	