1053_A. 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
from math import gcd
def tfit(n, m, No, Mo):
	if (n < m) != (No < Mo):
		n, m = m, n
	if n > No or m > Mo:
		return -1, -1
	return n, m
def sv():
	N, M, K = map(int, input().split())
	No = N
	Mo = M
	x = gcd(N, K)
	N //= x
	K //= x
	x = gcd(M, K)
	M //= x
	K //= x
	if K > 2:
		print('NO')
		return
	elif K == 2:
		Nres = N
		Mres = M
	elif K == 1:
		Nres, Mres = tfit(N*2, M, No, Mo)
		if Nres == -1:
			Nres, Mres = tfit(N, M*2, No, Mo)
			if Nres == -1:
				print('NO')
				return
	p = [(0,0) for i in range(3)]
	p[1] = [Nres, 0]
	p[2] = [0, Mres]
	print('YES')
	for i in range(3): print(' '.join(map(str, p[i])))
sv()

```