408351: GYM103104 B Mr.X and Reviewing Location

One day, while playing video games before the final exam, Mr. X suddenly remembered the afternoon when he first went to the General Library of Wuhan University. At that time, X's dormitory suffered a power failure. He went to the library just to borrow a novel to read. When X entered the library hall, he found that the library was full. There were many people standing in the rotunda(a round hall) reviewing because they didn't get a seat. X was shocked and ashamed, so he borrowed the book and hurried away.

Since then, the grades of X who didn't work hard have been widened by the top graders, and he faced increasing pressure to fail. Having recovered his spirit, X could not help but feel some regret for not studying hard at the beginning. Suddenly a golden light flashed on the computer screen and X found himself traveling back in time to the afternoon of his first visit to the main library. This time he wanted to join the revising crowd in the hall, study well and work hard.

X found that, although there were already many people in the hall, people automatically kept a certain distance between each other, at least $$$2.0$$$ meters away, to avoid mutual interference during the review. Given the location of the $$$n$$$ people in the hall and the radius $$$R$$$ of the rotunda (the center is at $$$(0,0)$$$), can you help little X find a place to review in the rotunda, and be at least $$$2.0$$$ meters away from the others?

The first line contains an integer $$$n\, (1 \leq n \leq 10^5)$$$, and a real number $$$R\, (1.0 \leq R \leq 1000.0)$$$, representing the number of people currently in the hall and the radius of the hall.

The next $$$n$$$ lines, two real numbers per line, representing the coordinates of the position of a person already in the hall.

It is guaranteed that the current distance between any two people is at least $$$2.0$$$ meters.

If the X cannot find the review location, print $$$\text{No}$$$, otherwise print $$$\text{Yes}$$$ on the first line, and print two real numbers representing the coordinates of the reviewing location found for X on the next line.

When there is a valid reviewing location for Mr.X, your answer would be considered correct if and only if the location you give is inside or on the border of the rotunda, and is at least $$$2.0$$$ meters away from the people currently in the hall, with the maximum absolute error of $$$10^{-6}$$$.

6 2.000000005
-1.000000000 -1.732050808
1.000000000 -1.732050808
-2.000000000 0.000000000
2.000000000 0.000000000
-1.000000000 1.732050808
1.000000000 1.732050808

Yes
-0.000000001 0.000000000

1 1.000000005
0.707106781 0.707100000

No