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.
def gcd(a, b):
	while b:
		a, b = b, a % b
	return a
n, m, k = map(int, input().split())
if n*m*2 % k:
	print("NO")
else:
	print("YES")
	g1 = gcd(n, k)
	n //= g1
	k //= g1
	g2 = gcd(m, k)
	m //= g2
	k //= g2
	if k == 1:
		if g1 == 1:
			m *= 2
		else:
			n *= 2
	print('0 0')
	print('0', m)
	print(n, '0')
