F. Exercise
time limit per test
6 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Gassa gave a new, interesting problem for the students in his class!

In this problem, he independently uniformly generated $$$n$$$ random points $$$(x_1; y_1), (x_2;y_2), \ldots, (x_n; y_n)$$$, each from the square $$$[0;10^9] \times [0;10^9]$$$.

After that, he independently uniformly generated two indices $$$i$$$, $$$j$$$, ($$$1 \leq i, j \leq n$$$), and set $$$k = x_i \cdot x_j + y_i \cdot y_j$$$.

And the goal is to find some pair of indices $$$i$$$, $$$j$$$, such that $$$x_i \cdot x_j + y_i \cdot y_j = k$$$.

Can you solve this problem?

Input

The first line of input contains two integers $$$n$$$ and $$$k$$$  — the number of points, and the scalar multiplication value $$$(1 \leq n \leq 200\,000, 0 \leq k \leq 2 \cdot 10^{18})$$$.

Each of the next $$$n$$$ lines contains two integers $$$x_i, y_i$$$ — the $$$i$$$-th point ($$$0 \leq x_i, y_i \leq 10^9$$$).

It is guaranteed that each of $$$x_i$$$ and $$$y_i$$$ is chosen randomly from the segment $$$[0;10^9]$$$.

Also, it is guaranteed that $$$k$$$ is equal to $$$x_i \cdot x_j + y_i \cdot y_j$$$ for some two random indices $$$i$$$,$$$j$$$.

Output

Output two integers $$$i$$$ and $$$j$$$, such that $$$(1 \leq i,j \leq n)$$$ and $$$x_i \cdot x_j + y_i \cdot y_j = k$$$.

If there are multiple possible answers, you can print any.

Scoring

SubtaskPointsConstraints
150$$$n \le 50\,000$$$
250$$$n \leq 200\,000$$$

Examples
Input
1 1476978419092933556
901418150 815121916
Output
1 1
Input
10 95652677520045149
805513144 38998401
16228409 266085559
293487744 471510400
138613792 649258082
904651590 244678415
443174087 503924246
579288498 219903162
179297759 762760972
92837851 728185679
983905980 299473031
Output
10 2