Vanya and Lanterns

题意翻译

### 题意简述 ⼀个⻓为$ L$ 的街道（左端点是 $0$，右端点是$ L$）上有 $n $个相 同的灯，第$ i$ 个灯放置的位置是 $a_i$。 - 问灯的半径⾄少要是多少，才能使得整个街道都有灯光。 ### 数据范围 - $ n \le 1000$，$L \le 10^9$

题目描述

Vanya walks late at night along a straight street of length $ l $ , lit by $ n $ lanterns. Consider the coordinate system with the beginning of the street corresponding to the point $ 0 $ , and its end corresponding to the point $ l $ . Then the $ i $ -th lantern is at the point $ a_{i} $ . The lantern lights all points of the street that are at the distance of at most $ d $ from it, where $ d $ is some positive number, common for all lanterns. Vanya wonders: what is the minimum light radius $ d $ should the lanterns have to light the whole street?

输入输出格式

输入格式

Vanya walks late at night along a straight street of length $ l $ , lit by $ n $ lanterns. Consider the coordinate system with the beginning of the street corresponding to the point $ 0 $ , and its end corresponding to the point $ l $ . Then the $ i $ -th lantern is at the point $ a_{i} $ . The lantern lights all points of the street that are at the distance of at most $ d $ from it, where $ d $ is some positive number, common for all lanterns. Vanya wonders: what is the minimum light radius $ d $ should the lanterns have to light the whole street?

输出格式

Print the minimum light radius $ d $ , needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed $ 10^{-9} $ .

输入输出样例

输入样例 #1

7 15
15 5 3 7 9 14 0

输出样例 #1

2.5000000000

输入样例 #2

2 5
2 5

输出样例 #2

2.0000000000

说明

Vanya walks late at night along a straight street of length $ l $ , lit by $ n $ lanterns. Consider the coordinate system with the beginning of the street corresponding to the point $ 0 $ , and its end corresponding to the point $ l $ . Then the $ i $ -th lantern is at the point $ a_{i} $ . The lantern lights all points of the street that are at the distance of at most $ d $ from it, where $ d $ is some positive number, common for all lanterns. Vanya wonders: what is the minimum light radius $ d $ should the lanterns have to light the whole street?