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.

n, m, k = map(int, input().split())
s = n*m / k

def gcd(a,b):
	if b == 0:
		return a
	else:
		return gcd(b, a%b)


if 2*n*m % k == 0:
	f = True
	if(k % 2 == 0):
		k //= 2
		f = False
	
	print("YES")
	a = n / gcd(n, k)
	b = m*gcd(n, k) / k

	if(f):
		if(a < n): a *= 2;
		else: b *= 2;

	print(0,0)
	print(0,int(b))
	print(int(a),0)

else:
	print("NO")
