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 collections import defaultdict

def generate(factors, arr, ind, current):
	if ind == len(arr):
		factors.add(current)
		return
	num = 1
	for i in range(arr[ind][1]+1):
		generate(factors, arr, ind+1, current*num)
		num *= arr[ind][0]

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

orin = n
orim = m
orik = k

x1, y1, x3, y2 = 0, 0, 0, 0

nprimes = defaultdict(int)
mprimes = defaultdict(int)
kprimes = defaultdict(int)

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

curnum = 2
while curnum <= int(n**0.5):
	while n%curnum == 0:
		nprimes[curnum] += 1
		n //= curnum
	curnum += 1;


if n != 1:
	nprimes[n] += 1

curnum = 2
while curnum <= int(m**0.5):
	while m%curnum == 0:
		mprimes[curnum] += 1
		m //= curnum
	curnum += 1;
if m != 1:
	mprimes[m] += 1

curnum = 2
while curnum <= int(k**0.5):
	while k%curnum == 0:
		kprimes[curnum] += 1
		k //= curnum
	curnum += 1;
if k != 1:
	kprimes[k] += 1

# print(kprimes)

for x in mprimes:
	nprimes[x] += mprimes[x]

nprimes[2] += 1
for x in kprimes:
	nprimes[x] -= kprimes[x]


factors = set()
arr = []
for x in nprimes:
	if nprimes[x] != 0:
		arr += [[x, nprimes[x]]]

generate(factors, arr, 0, 1)

numerator = 2*orin*orim//orik

x2, y3 = -1, -1
for x in factors:
	if x <= orin and numerator//x <= orim:
		x2, y3 = x, numerator//x
	elif x <= orim and numerator//x <= orin:
		y3, x2 = x, numerator//x

# print(factors)

if x2 == -1:
	print("NO")
else:
	print("YES")
	print(x1, y1)
	print(x2, y2)
	print(x3, y3)






