CF1468I Plane Tiling

You are given five integers $ n $ , $ dx_1 $ , $ dy_1 $ , $ dx_2 $ and $ dy_2 $ . You have to select $ n $ distinct pairs of integers $ (x_i, y_i) $ in such a way that, for every possible pair of integers $ (x, y) $ , there exists exactly one triple of integers $ (a, b, i) $ meeting the following constraints: $ \begin{cases} x \, = \, x_i + a \cdot dx_1 + b \cdot dx_2, \\ y \, = \, y_i + a \cdot dy_1 + b \cdot dy_2. \end{cases} $

The first line contains a single integer $ n $ ( $ 1 \le n \le 10^5 $ ). The second line contains two integers $ dx_1 $ and $ dy_1 $ ( $ -10^6 \le dx_1, dy_1 \le 10^6 $ ). The third line contains two integers $ dx_2 $ and $ dy_2 $ ( $ -10^6 \le dx_2, dy_2 \le 10^6 $ ).

If it is impossible to correctly select $ n $ pairs of integers, print NO. Otherwise, print YES in the first line, and then $ n $ lines, the $ i $ -th of which contains two integers $ x_i $ and $ y_i $ ( $ -10^9 \le x_i, y_i \le 10^9 $ ). If there are multiple solutions, print any of them.