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

n, m, k = map(int, input().split())
n1, m1, k1=n, m, k
f=0
if (2*m*n)%k!=0:
  print ("NO")
else:
  f=0
  if k%2==0:
    k=k//2
    f=1
  t=gcd(n, k)
  while t!=1:
    n=n//t
    k=k//t
    t=gcd(n, k)
  t=gcd(m, k)
  while t!=1:
    m=m//t
    k=k//t
    t=gcd(m, k)
  if f==0:
    if m*2<=m1:
      m*=2
      print ("YES")
      print ('0 0')
      print (0, m)
      print (n, 0)
    else:
      if n*2<=n1:
        n*=2
        print ("YES")
        print ('0 0')
        print (0, m)
        print (n, 0)
      else:
        print ('NO')
  else:
    if n<=n1 and m<=m1:
      print ("YES")
      print ('0 0')
      print (0, m)
      print (n, 0)
    else:
      print ("NO")