492B. Vanya and Lanterns

binary search/implementation/math/sortings, 1200, https://codeforces.com/problemset/problem/492/B

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?

Input

The first line contains two integers $n$, $l$ (1 ≤ n ≤ 1000, 1 ≤ $l$ ≤ 10^9^) — the number of lanterns and the length of the street respectively.

The next line contains n integers a~i~ (0 ≤ a~i~ ≤ $l$). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.

Output

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^.

Examples

input

7 15
15 5 3 7 9 14 0

output

2.5000000000

input

2 5
2 5

output

2.0000000000

Note

Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.

n,l=map(int,input().split())
a=list(map(int,input().split()))
ans=0
a.sort()
for i in range(n-1):
    ans = max(ans, (a[i+1]-a[i])/2)
print(max(ans, a[0], l-a[-1]))