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
input=lambda : stdin.readline().strip()
lin=lambda :list(map(int,input().split()))
iin=lambda :int(input())
main=lambda :map(int,input().split())
from math import ceil,sqrt,factorial,log
from collections import deque
from bisect import bisect_left
def gcd(a,b):
	a,b=max(a,b),min(a,b)
	while a%b!=0:
		a,b=b,a%b
	return b
def solve():
	n,m,k=main()
	if (2*m*n)%k!=0:
		print("NO")
	else:
		t=(2*n*m)//k
		print("YES")
		print(0,0)
		x=0
		y=0
		f=0
		if k%2==0:
			k=k//2
			f=1
		x=gcd(n,k)
		k=k//x
		a=n//x
		x=gcd(m,k)
		k=k//x
		b=m//x
		if f==0:
			if a<n:
				a+=a
			else:
				b+=b
		print(a,0)
		print(0,b)

qwe=1
# qwe=int(input())
for _ in range(qwe):
	solve()
