A14028. 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.