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 a != 0 and b != 0:
		if a > b:
			a %= b
		else:
			b %= a
	return a + b

s = input().split(' ')
n = int(s[0])
m = int(s[1])
k = int(s[2])

divided = False

if 2 * n * m % k != 0:
	print("NO")
	exit()

if k % 2 == 0:
	k = k // 2
	divided = True

k1 = GCD(n,k);
k2 = k // k1;
x = n // k1;
y = m // k2;
if not divided:
	if 2 * x <= n:
		x *= 2
	elif 2 * y <= m:
		y *= 2
	else:
		print("NO")
		exit()

print("YES")
print(0, y)
print(0, 0)
print(x, 0)