Random problem#11127
Marty decided to distract his friend Alex from thinking about juicy steaks and entertain him with one interesting puzzle.
First, he randomly chose points (x_i, y_i) (0 \leq x_i, y_i \leq 10^9). Then, he randomly chose two indices and (1 \leq i, j \leq n) with equal probability. After that, he calculated the value k = x_i \cdot x_j + y_i \cdot y_j.
Now he gave Alex points and the number . And asks him to find any pair of indices and such that x_a \cdot x_b + y_a \cdot y_b = k. Alex does not want to solve this problem, so help him.
The first line contains two integers and (1 \leq n \leq 200\,000, 0 \leq k \leq 2 \cdot 10^{18}).
The next lines contain two integers x_i and y_i the coordinates of the -th point (0 \leq x_i, y_i \leq 10^9). It is guaranteed that the points were generated randomly with equal probability.
It is guaranteed that was evaluated as x_i \cdot x_j + y_i \cdot y_j, where and were chosen randomly with equal probability.
Print two integers and (1 \leq a, b \leq n) such that x_a \cdot x_b + y_a \cdot y_b = k. If there are several suitable answers, you can print any one.
Example 1
Example 2