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.
#!/usr/bin/env python3
import sys
from math import gcd

def rint():
    return map(int, sys.stdin.readline().split())
#lines = stdin.readlines()

n, m, k = rint()

if (2*n*m)%k:
    print("NO")
    exit()

nk_gcd = gcd(n, k)

w = n//nk_gcd
k = k//nk_gcd

mk_gcd = gcd(m, k)

h = m//mk_gcd
k = k//mk_gcd

if k == 1:
    if w < n:
        w *= 2
    elif h < m:
        h *= 2
else:
    # In order to 2*n*m/k is integer, k is 2, so no need to divide  w or h by 2
    pass

print("YES")
print(0, 0)
print(w, 0)
print(0, h)
