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 fractions import gcd
n,m,k = map(int,raw_input().split())
t = 2
if (2*n*m)%k:
    print "NO"
else:
    h = m
    b = n
    x = gcd(h,k)
    h = h/x
    k = k/x
    
    x = gcd(b,k)
    b = b/x
    k = k/x
    
    x = gcd(t,k)
    t = t/x
    k = k/x
    
    if h < m : h = t*h
    else: b = t*b
    
    print "YES"
    print 0,0
    print b,0
    print 0,h