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 gcd(a,b):
	while b: a,b = b,a%b
	return a
	
def solve(N,M,k,n,m):
	if (N*M)%k != 0: return None
	g = gcd(N,k)
	ng = N/g
	mg = M/(k/g)
	x = ng
	y = mg
	if x <= n and y <= m and x*y*k == N*M: return x,y
	return None
	
n,m,k = map(int,raw_input().split())
if solve(2*n,m,k,n,m):
	x,y = solve(2*n,m,k,n,m)
	print "YES"
	print 0,0
	print x,0
	print 0,y
elif solve(2*m,n,k,m,n):
	y,x = solve(2*m,n,k,m,n)
	print "YES"
	print 0,0
	print x,0
	print 0,y
else:
	print "NO"