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 __future__ import print_function
 
import sys
 
from fractions import gcd
 
N, M, k = [int(x) for x in raw_input().split()]
 
g1 = gcd(N, k)
n, k = N//g1, k//g1
 
g2 = gcd(M, k)
m, k = M//g2, k//g2
 
if k > 2:
        print("NO")
        sys.exit()
 
if k == 1:
        if n * m * 2 > N * M: # larger than half the N*M-rectangle, impossible.
                print("NO")
                sys.exit()
        if n <= N//2:
                n, k = n*2, k*2
        elif m <= M//2:
                m, k = m*2, k*2
        else: 
                assert False # should never happen, because we divide stuff away from N, M
x1, y1 = 0, 0
x2, y2 = n, 0
x3, y3 = 0, m
print("YES")
print(x1, y1)
print(x2, y2)
print(x3, y3)