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.
from sys import stdin, stdout
input = stdin.buffer.readline
#print = stdout.write

n, m, k = map(int, input().split())
if 2 * n * m % k == 0:
	i = 2
	t = k
	N = n
	while i * i <= k:
		while t % i == 0 and (n % i == 0 or m % i == 0):
			t //= i
			if n % i == 0:
				n //= i
			else:
				m //= i
		i += 1
	if t % 2:
		if t > 1:
			if n % t == 0:
				n //= t
			else:
				m //= t
		if n * 2 <= N:
			n *= 2
		else:
			m *= 2
	else:
		t //= 2
		if t > 1:
			if n % t == 0:
				n //= t
			else:
				m //= t
		
	print('YES')
	print(0, 0)
	print(n, 0)
	print(0, m)
else:
	print('NO')
