CF1030D.Vasya and Triangle

普及/提高-

通过率：0%

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题目描述

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 $0 \le x_1, x_2, x_3 \le n$ , $0 \le y_1, y_2, y_3 \le m$ 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.

输入格式

The single line contains three integers $n$ , $m$ , $k$ ( $1\le n, m \le 10^9$ , $2 \le k \le 10^9$ ).

输出格式

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).

输入输出样例

输入#1
```
4 3 3
```
输出#1
```
YES
1 0
2 3
4 1
```
输入#2
```
4 4 7
```
输出#2
```
NO
```

说明/提示

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 $\frac{nm}{k} = \frac{16}{7}$ .

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