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Vanya walks down a street of length 'l' meters, along which 'n' lanterns are placed at various positions. Each lantern lights an area centered at its position. The goal is to determine the minimum radius 'r' needed for each lantern's light so that the entire street, from 0 to 'l', is completely illuminated.
The first line contains two integers n and l (1 ≤ n ≤ 10^5, 1 ≤ l ≤ 10^9) — the number of lanterns and the length of the street. The second line contains n integers a_i (0 ≤ a_i ≤ l) — the positions of the lanterns on the street.
Print a single floating point number — the minimum radius 'r' needed for each lantern so that the street is fully lit. Your answer will be considered correct if its absolute or relative error does not exceed 10^-9.
1 ≤ n ≤ 10^5; 1 ≤ l ≤ 10^9; 0 ≤ a_i ≤ l.
Example 1
Input
7 15 15 5 3 7 9 14 0
Output
2.5
Explanation
After sorting, lantern positions: 0, 3, 5, 7, 9, 14, 15. The largest gap between lanterns is 5 (between 9 and 14), so half is 2.5. The gaps at ends: between 0 and start is 0, between 15 and 15 is 0. Maximum radius is 2.5.