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D. Vasya and Triangle

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya 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 $$$0 \le x_1, x_2, x_3 \le n$$$, $$$0 \le y_1, y_2, y_3 \le m$$$ and the area of the triangle formed by these points is equal to $$$\frac{nm}{k}$$$.

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 $$$n$$$, $$$m$$$, $$$k$$$ ($$$1\le n, m \le 10^9$$$, $$$2 \le k \le 10^9$$$).

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 $$$\frac{nm}{k} = 4$$$. The triangle mentioned in the output is pictured below:

In the second example there is no triangle with area $$$\frac{nm}{k} = \frac{16}{7}$$$.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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