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 sys

# def gdc(k, n):
# 	"""
# 	"""
# 	divisor = 0
# 	for i in range(1, max([k, n]) + 1):
# 		if k % i == 0 and \
# 			n % i == 0:
# 			divisor = i

# 	return divisor

def gcd(a, b):
    """Calculate the Greatest Common Divisor of a and b.

    Unless b==0, the result will have the same sign as b (so that when
    b is divided by it, the result comes out positive).
    """
    while b:
        a, b = b, a%b
    return a

def find(upper_x, upper_y, k):
	"""
	ref: https://www.mathopenref.com/coordtrianglearea.html
	ref: http://codeforces.com/blog/entry/62013
	s = upper_x * upper_y / k
	"""
	if upper_x * upper_y * 2 % k != 0: return None
	if k % 2 == 0:
		k = k / 2
		divisor = gcd(k, upper_x)
		a = upper_x / divisor
		_k = k / divisor
		b = m / _k
		return (0, 0), (a, 0), (0, b)
	else:
		divisor = gcd(k, upper_x)
		a = upper_x / divisor
		_k = k / divisor
		b = m / _k
		if a < upper_x:
			a = a * 2
		else:
			b = b * 2
		return (0, 0), (a, 0), (0, b)

data = []
for line in sys.stdin:
	line = line.strip("\n\r").split(" ")
	data = [int(ele) for ele in line]
	break

n, m, k = data
res = find(n, m, k)
if res is None:
	print "NO"
else:
	print "YES"
	for ele in res:
		print ele[0], ele[1]