1030_D. Vasya and Triangle
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.
```python
# import math

n, m, k = [int(x) for x in input().split()]
a = n
b = k
if (2 * n * m) % k != 0:
	print("no")
else:
	c = a % b
	while (c != 0):
		a = b
		b = c
		c = a % b
	# print(b)
	# b is GCD
	if b == 1:
		x = n
		y = 2 * m // k
	else:
		if b != k:
			x = n // b
			y = 2 * m // (k // b)
		else:
			x = 2 * n // b
			y = m // (k // b)

	print('yes')
	print(0, 0)
	print(x, 0)
	print(0, y)

```