시간 제한메모리 제한제출정답맞힌 사람정답 비율
4 초 512 MB4881209329.430%

## 문제

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?

## 입력

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 xi and yi of the ith candle in nanometers, separated with a space.

Limits

• 3 ≤ N ≤ 2 · 105;
• 10 ≤ R ≤ 2 · 108;
• for 1 ≤ i ≤ N, xi2 + yi2 ≤ R2;
• all points have distinct coordinates.

## 출력

Print the value W as a floating point number. An additive or multiplicative error of 10−5 is tolerated: if y is the answer, any number either within [y − 10−5 ; y + 10−5] or within [(1 − 10−5)y;(1 + 10−5)y] is accepted.

## 예제 입력 1

3 10
0 0
10 0
0 10


## 예제 출력 1

7.0710678118654755