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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;
import java.util.function.Function;

public class P492B {

    static boolean multipleIndependent = false;

    void run() {
        int n = in.nextInt();
        int l = in.nextInt();
        int[] a = in.nextIntArray(n);
        Arrays.sort(a);
        double max = Math.max(a[0], l - a[n - 1]);
        for (int i = 1; i < n; i++) {
            max = Math.max(max, (a[i] - a[i - 1]) / 2.0);
        }
        System.out.println(max);
    }


    /* -----: Template :----- */
    static InputReader in = new InputReader(System.in);

    public static void main(String[] args) {
        P492B p = new P492B();
        int q = multipleIndependent ? in.nextInt() : 1;
        while (q-- > 0) {
            p.run();
        }
    }

    int numLength(long n) {
        int l = 0;
        while (n > 0) {
            n /= 10;
            l++;
        }
        return l;
    }

    <R> long binarySearch(long lowerBound, long upperBound,
            R value, Function<Long, R> generatorFunction, Comparator<R> comparator) {
        if (lowerBound <= upperBound) {
            long mid = (lowerBound + upperBound) / 2;
            int compare = comparator.compare(generatorFunction.apply(mid), value);
            if (compare == 0) {
                return mid;
            } else if (compare < 0) {
                return binarySearch(mid + 1, upperBound, value, generatorFunction, comparator);
            } else {
                return binarySearch(lowerBound, mid - 1, value, generatorFunction, comparator);
            }
        } else {
            return -1;
        }
    }

    <T> Integer[] sortSimultaneously(T[] key, Comparator<T> comparator,
            Object[]... moreArrays) {
        int n = key.length;
        for (Object[] array : moreArrays) {
            if (array.length != n) {
                throw new RuntimeException("Arrays must have equals lengths");
            }
        }
        Integer[] indices = new Integer[n];
        for (int i = 0; i < n; i++) {
            indices[i] = i;
        }
        Comparator<Integer> delegatingComparator = (a, b) -> {
            return comparator.compare(key[a], key[b]);
        };
        Arrays.sort(indices, delegatingComparator);
        reorder(indices, key);
        for (Object[] array : moreArrays) {
            reorder(indices, array);
        }
        return indices;
    }

    void reorder(Integer[] indices, Object[] arr) {
        if (indices.length != arr.length) {
            throw new RuntimeException("Arrays must have equals lengths");
        }
        int n = arr.length;
        Object[] copy = new Object[n];
        for (int i = 0; i < n; i++) {
            copy[i] = arr[indices[i]];
        }
        System.arraycopy(copy, 0, arr, 0, n);
    }

    int prodMod(int a, int b, int mod) {
        return (int) (((long) a) * b % mod);
    }

    long prodMod(long a, long b, long mod) {
        long res = 0;
        a %= mod;
        b %= mod;
        while (b > 0) {
            if ((b & 1) > 0) {
                res = (res + a) % mod;
            }
            a = (a << 1) % mod;
            b >>= 1;
        }
        return res;
    }

    long sumMod(int[] b, long mod) {
        long res = 0;
        for (int i = 0; i < b.length; i++) {
            res = (res + b[i] % mod) % mod;
        }
        return res;
    }

    long sumMod(long[] a, long mod) {
        long res = 0;
        for (int i = 0; i < a.length; i++) {
            res = (res + a[i] % mod) % mod;
        }
        return res;
    }

    long sumProdMod(int[] a, long b, long mod) {
        long res = sumMod(a, mod);
        return prodMod(res, b, mod);
    }

    long sumProdMod(long[] a, long b, long mod) {
        long res = sumMod(a, mod);
        return prodMod(res, b, mod);
    }

    long sumProdMod(int[] a, int[] b, long mod) {
        if (a.length != b.length) {
            throw new RuntimeException("Arrays must have equals lengths");
        }
        long res = 0;
        for (int i = 0; i < a.length; i++) {
            res = (res + prodMod(a[i], b[i], mod)) % mod;
        }
        return res;
    }

    long sumProdMod(long[] a, long[] b, long mod) {
        if (a.length != b.length) {
            throw new RuntimeException("Arrays must have equals lengths");
        }
        long res = 0;
        for (int i = 0; i < a.length; i++) {
            res = (res + prodMod(a[i], b[i], mod)) % mod;
        }
        return res;
    }

    int[] toPrimitive(Integer[] arr) {
        int[] res = new int[arr.length];
        for (int i = 0; i < arr.length; i++) {
            res[i] = arr[i];
        }
        return res;
    }

    int[][] toPrimitive(Integer[][] arr) {
        int[][] res = new int[arr.length][];
        for (int i = 0; i < arr.length; i++) {
            res[i] = toPrimitive(arr[i]);
        }
        return res;
    }

    long[] toPrimitive(Long[] arr) {
        long[] res = new long[arr.length];
        for (int i = 0; i < arr.length; i++) {
            res[i] = arr[i];
        }
        return res;
    }

    long[][] toPrimitive(Long[][] arr) {
        long[][] res = new long[arr.length][];
        for (int i = 0; i < arr.length; i++) {
            res[i] = toPrimitive(arr[i]);
        }
        return res;
    }

    Integer[] toWrapper(int[] arr) {
        Integer[] res = new Integer[arr.length];
        for (int i = 0; i < arr.length; i++) {
            res[i] = arr[i];
        }
        return res;
    }

    Integer[][] toWrapper(int[][] arr) {
        Integer[][] res = new Integer[arr.length][];
        for (int i = 0; i < arr.length; i++) {
            res[i] = toWrapper(arr[i]);
        }
        return res;
    }

    Long[] toWrapper(long[] arr) {
        Long[] res = new Long[arr.length];
        for (int i = 0; i < arr.length; i++) {
            res[i] = arr[i];
        }
        return res;
    }

    Long[][] toWrapper(long[][] arr) {
        Long[][] res = new Long[arr.length][];
        for (int i = 0; i < arr.length; i++) {
            res[i] = toWrapper(arr[i]);
        }
        return res;
    }

    static class InputReader {

        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public <T> T[] nextIntArray(int n, Function<Integer, T> function, Class<T> c) {
            T[] arr = (T[]) Array.newInstance(c, n);
            for (int i = 0; i < n; i++) {
                arr[i] = function.apply(nextInt());
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        public <T> T[] nextLongArray(int n, Function<Long, T> function, Class<T> c) {
            T[] arr = (T[]) Array.newInstance(c, n);
            for (int i = 0; i < n; i++) {
                arr[i] = function.apply(nextLong());
            }
            return arr;
        }

        public int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = nextIntArray(m);
            }
            return map;
        }

        public long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = nextLongArray(m);
            }
            return map;
        }

        public char[][] nextCharMap(int n) {
            char[][] map = new char[n][];
            for (int i = 0; i < n; i++) {
                map[i] = next().toCharArray();
            }
            return map;
        }

        public void readColumns(Object[]... columns) {
            int n = columns[0].length;
            for (Object[] column : columns) {
                if (column.length != n) {
                    throw new RuntimeException("Arrays must have equals lengths");
                }
            }
            for (int i = 0; i < n; i++) {
                for (Object[] column : columns) {
                    column[i] = read(column[i].getClass());
                }
            }
        }

        public <T> T read(Class<T> c) {
            throw new UnsupportedOperationException("To be implemented");
        }

    }

}