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 prime_factors(n):
	i = 2
	factors = []
	while i * i <= n:
		if n % i:
			i += 1
		else:
			n //= i
			factors.append(i)
	if n > 1:
		factors.append(n)
	return factors

def factors(n):
	super=[1]
	for i in prime_factors(n):
		super.extend([j*i for j in super])
	return list(sorted(set(super)))

def answer(h,w,h1,w2):
	print("YES")
	if m>=n:
		h,w=max(h,w),min(h,w)
		h1,w2=max(h1,w2),min(h1,w2)
	else:
		w,h=max(h,w),min(h,w)
		w2,h1=max(h1,w2),min(h1,w2)
	print("0 0")
	print("{} {}".format(w-w2,h1))
	print("{} {}".format(w2,h-h1))

n,m,k=map(int,input().split())
h=n
w=m
if n*m*2%k!=0:
	print("NO")
	quit()
else:
	list_1=prime_factors(k)
	for i in range(len(list_1)-1,-1,-1):
		if h%list_1[i]==0:
			h//=list_1[i]
			list_1.pop(i)
	for i in range(len(list_1)-1,-1,-1):
		if w%list_1[i]==0:
			w//=list_1[i]
			list_1.pop(i)
	h1,w2=0,0
	if not list_1:
		if 2*h<=n:
			h*=2
		elif 2*w<=m:
			w*=2
	answer(h,w,h1,w2)
		