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:
\( \begin{cases} x \, = \, x_i + a \cdot dx_1 + b \cdot dx_2, \\ y \, = \, y_i + a \cdot dy_1 + b \cdot dy_2. \end{cases} \) 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.
Примеры
| № | Входные данные | Выходные данные |
|
1
|
4
2 0
0 2
|
YES
0 0
0 1
1 0
1 1
|
|
2
|
5
2 6
1 5
|
NO
|
|
3
|
2
3 4
1 2
|
YES
0 0
0 1
|