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.
p=input().split()
n=int(p[0])
m=int(p[1])
k=int(p[2])
cnt=0
if (2*n*m%k)!=0:
  print('NO')
else:
  print('YES')
  if k%2==0:
    k//=2
    cnt=1
  n1=n
  k1=k
  if n1<k1:
    n1,k1=k1,n1
  while k1!=0:
    n1,k1=k1,n1%k1
  kk=k/n1
  a=n/n1
  b=m/kk
  if cnt==0:
    if a<n:
      a*=2
    else:
      b*=2
  a=int(a)
  b=int(b)
  print(0,0)
  print(a,0)
  print(0,b)