Problem: 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 ai. 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 ≤ 109) — the number of lanterns and the length of the street respectively. 

The next line contains n integers ai (0 ≤ ai ≤ 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.

Solution (in JAVA):

Solution:
        import java.io.*;
        import java.util.*;
        import java.math.*;
        import java.text.*;
         
        public class bhaa {
         
            InputStream is;
            PrintWriter o;
            /////////////////// CODED++ BY++ ++ ++ ++ BHAVYA++ ARORA++ ++ ++ ++ FROM++ JAYPEE++ INSTITUTE++ OF++ INFORMATION++ TECHNOLOGY++ ////////////////
         
        ///////////////////////// Make it work, make it right, make it fast. Make it work, make it right, make it fast. Make it work, make it right, make it fast. Make it work, make it right, make it fast. /////////////////
         
          
            int bs(int arr[],int l,int r,int x)
            {
                if(l<=r)
                {
                    int mid=(l+r)/2;
                    if(arr[mid]==x)
                    {
                        return mid;
                    }
                    if(x>arr[mid])
                    {
                        return bs(arr,mid+1,r,x);
                    }
                    if(x<arr[mid])
                    {
                        return bs(arr,l,mid-1,x);
                    }


                }
                return -1;

            }
            int su(int n)
            {
                int s=0;
                while(n!=0)
                {
                    s+=n%10;
                    n/=10;
                }
                return s;
            }

           
            void solve() {


            int n=ni();
            int m=ni();
            int arr[]=nia(n);
            Arrays.sort(arr);

            int st=arr[0];
            int end=arr[n-1];
            double maxm=0;
            
            DecimalFormat df=new DecimalFormat("#.0000000000");

            int f=0;
            double prev=arr[0];
           for(int i=1;i<n;i++)
           {
                double diff=(arr[i]-prev)*1.0/2;
                maxm=Math.max(maxm,diff);
                prev=arr[i];

           }
            //o.println(maxm+" "+st+" "+end)
;          o.println(df.format(Math.max(maxm,Math.max(m-end,st))));


           
                
         
         
                
                
         
            }
         
         
         
         
         
         
           
         
         
            
         
         
         
         
         
         
         
         
         
         
         
         
            
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
            //---------- I/O Template ----------
            
            public static void main(String[] args) { new bhaa().run(); }
            void run() { 
                is = System.in; 
                o = new PrintWriter(System.out);
                solve();
                o.flush();
            }
            
            byte input[] = new byte[1024];
            int len = 0, ptr = 0;
            
            int readByte() { 
                if(ptr >= len) { ptr = 0; 
                    try { len = is.read(input); } 
                    catch(IOException e) { throw new InputMismatchException(); } 
                    if(len <= 0) { return -1; } 
                } return input[ptr++];
            }
            boolean isSpaceChar(int c) { return !( c >= 33 && c <= 126 ); }
            int skip() { 
                int b = readByte(); 
                while(b != -1 && isSpaceChar(b)) { b = readByte(); } 
                return b;
            }
            
            char nc() { return (char)skip(); }
            String ns() { 
                int b = skip(); 
                StringBuilder sb = new StringBuilder(); 
                while(!isSpaceChar(b)) { sb.appendCodePoint(b); b = readByte(); } 
                return sb.toString();
            }
            String nLine() { 
                int b = skip(); 
                StringBuilder sb = new StringBuilder(); 
                while( !(isSpaceChar(b) && b != ' ') ) { sb.appendCodePoint(b); b = readByte(); } 
                return sb.toString();
            }
            int ni() { 
                int n = 0, b = readByte(); 
                boolean minus = false; 
                while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')) { b = readByte(); } 
                if(b == '-') { minus = true; b = readByte(); } 
                if(b == -1) { return -1; }  //no input 
                while(b >= '0' && b <= '9') { n = n * 10 + (b - '0'); b = readByte(); } 
                return minus ? -n : n;
            }
            long nl() { 
                long n = 0L;    int b = readByte(); 
                boolean minus = false; 
                while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')) { b = readByte(); } 
                if(b == '-') { minus = true; b = readByte(); } 
                while(b >= '0' && b <= '9') { n = n * 10 + (b - '0'); b = readByte(); } 
                return minus ? -n : n;
            }
         
            double nd() { return Double.parseDouble(ns()); }
            float nf() { return Float.parseFloat(ns()); }
            int[] nia(int n) { 
                int a[] = new int[n]; 
                for(int i = 0; i < n; i++) { a[i] = ni(); } 
                return a;
            }
            long[] nla(int n) { 
                long a[] = new long[n]; 
                for(int i = 0; i < n; i++) { a[i] = nl(); } 
                return a;
            }
            int [][] nim(int n)
            {
                int mat[][]=new int[n][n];
                for(int i=0;i<n;i++)
                {
                    for(int j=0;j<n;j++)
                    {
                        mat[i][j]=ni();
                    }
                }
                return mat;
            }
            long [][] nlm(int n)
            {
                long mat[][]=new long[n][n];
                for(int i=0;i<n;i++)
                {
                    for(int j=0;j<n;j++)
                    {
                        mat[i][j]=nl();
                    }
                }
                return mat;
            }
            
         
         
         
         
            
            char[] ns(int n) { 
                char c[] = new char[n]; 
                int i, b = skip(); 
                for(i = 0; i < n; i++) { 
                    if(isSpaceChar(b)) { break; } 
                    c[i] = (char)b; b = readByte(); 
                } return i == n ? c : Arrays.copyOf(c,i);
            }
            void piarr(int arr[])
            {
                for(int i=0;i<arr.length;i++)
                {
                    o.print(arr[i]+" ");
         
                }
                o.println();
            }
            void plarr(long arr[])
            {
                for(int i=0;i<arr.length;i++)
                {
                    o.print(arr[i]+" ");
         
                }
                o.println();
            }
            
            void pimat(int mat[][])
            {
                for(int i=0;i<mat.length;i++)
                {
                    for(int j=0;j<mat[0].length;j++)
                    {
                        o.print(mat[i][j]);
                    }
                    o.println();
                }
            }
            void plmat(long mat[][])
            {
                for(int i=0;i<mat.length;i++)
                {
                    for(int j=0;j<mat[0].length;j++)
                    {
                        o.print(mat[i][j]);
                    }
                    o.println();
                }
         
            }
         
         
         
         
            //////////////////////////////////// template finished //////////////////////////////////////
         
         
         
        }