As Jacques-Édouard really likes birthday cakes, he celebrates his birthday every hour, instead of every year. His friends ordered him a round cake from a famous pastry shop, and placed candles on its top surface. The number of candles equals the age of Jacques-Édouard in hours. As a result, there is a huge amount of candles burning on the top of the cake. Jacques-Édouard wants to blow all the candles out in one single breath.

You can think of the flames of the candles as being points in the same plane, all within a disk of radius ~R~ (in nanometers) centered at the origin. On that same plane, the air blown by Jacques-Édouard follows a trajectory that can be described by a straight strip of width ~W~, which comprises the area between two parallel lines at distance ~W~, the lines themselves being included in that area. What is the minimum width ~W~ such that Jacques-Édouard can blow all the candles out if he chooses the best orientation to blow?

Input Specification

The first line consists of the integers ~N~ and ~R~, separated with a space, where ~N~ is Jacques-Édouard's age in hours. Then ~N~ lines follow, each of them consisting of the two integer coordinates ~x_i~ and ~y_i~ of the ~i^{th}~ candle in nanometers, separated with a space.

Constraints

• ~3 \le N \le 2 \cdot 10^5~;
• ~10 \le R \le 2 \cdot 10^8~;
• for ~1 \le i \le N~, ~x_i^2 + y_i^2 \le R^2~;
• all points have distinct coordinates.

Output Specification

Print the value ~W~ as a floating point number. Your answer will be considered correct if it has an absolute or relative error of at most ~10^{-5}~.

Sample Input

3 10
0 0
10 0
0 10

Sample Output

7.0710678118654755