Plane Tiling

1000ms

524288K

Description:

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:

$$$ \begin{cases} x \, = \, x_i + a \cdot dx_1 + b \cdot dx_2, \\ y \, = \, y_i + a \cdot dy_1 + b \cdot dy_2. \end{cases} $$$

Input:

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 $$$dy_2$$$ ($$$-10^6 \le dx_2, dy_2 \le 10^6$$$).

Output:

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.

Sample Input:

4
2 0
0 2

Sample Output:

Sample Input:

5
2 6
1 5

Sample Output:

NO

Sample Input:

2
3 4
1 2

Sample Output:

YES
0 0
0 1

Informação

Provedor Codeforces

Código CF1468I