Vasya and Triangle

题意翻译

给定$1 \le n,m \le 10^9$，$2 \le k \le 10^9$，求出三个点$A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)$，满足： 1. $0 \le x_1,x_2,x_3 \le n$，$0 \le y_1,y_2,y_3 \le m$ 1. $S_{\Delta}ABC=\frac{nm}{k}$ 若无解则直接输出`NO`，否则第一行输出`YES`，接下来的三行为三个点的坐标。

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.

输入输出格式

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

输入样例 #1

4 3 3

输出样例 #1

YES
1 0
2 3
4 1

输入样例 #2

4 4 7

输出样例 #2

NO

说明

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} $ .

题意翻译

给定$1 \le n,m \le 10^9$，$2 \le k \le 10^9$，求出三个点$A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)$，满足： 1. $0 \le x_1,x_2,x_3 \le n$，$0 \le y_1,y_2,y_3 \le m$ 1. $S_{\Delta}ABC=\frac{nm}{k}$ 若无解则直接输出`NO`，否则第一行输出`YES`，接下来的三行为三个点的坐标。