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.math.BigInteger;
import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static Scanner scanner = new Scanner(System.in);

    public static void main(String[] args) {
        int n = scanner.nextInt();
        int l = scanner.nextInt();
        int[] array = new int[n];
        for (int i = 0; i < n; i++) {
            array[i] = scanner.nextInt();
        }
        Arrays.sort(array);
        double max = 0;
        for (int i = 0; i < array.length - 1; i++) {
            double temp = ((double) (array[i + 1] - array[i]) )/ 2;
            if (temp > max) {
                max = temp;
            }
        }
        System.out.printf("%.9f", Math.max(Math.max(l - array[array.length - 1], max), array[0]));
    }

    public static int binarySearchMod(int arr[], int first, int last, int key) {
        if (arr.length == 1) {
            if (arr[0] <= key) {
                return 1;
            }
            return 0;
        }
        if (arr[0] <= key && arr[1] > key) {
            return 1;
        }
        if (arr[0] > key) {
            return 0;
        }
        if (arr[arr.length - 1] <= key) {
            return arr.length;
        }

        while (true) {
            int mid = (first + last) / 2;
            if (mid + 1 == arr.length) {
                return mid;
            }
            if (arr[mid] <= key && arr[mid + 1] > key) {
                return mid + 1;
            }
            if (arr[mid] > key) {
                last = mid;
                continue;
            }
            if (arr[mid] <= key) {
                first = mid;
            }
        }
    }

    public static BigInteger printFibonacciWithoutArrays(int n) {
        if (n == 0) {
            return BigInteger.ZERO;
        }
        if (n == 1) {
            return BigInteger.ONE;
        }
        BigInteger prevOfPrev = BigInteger.ZERO;
        BigInteger prev = BigInteger.ONE;
        BigInteger now = BigInteger.ZERO;
        for (int i = 2; i <= n; i++) {
            now = prevOfPrev.add(prev);
            prevOfPrev = prev;
            prev = now;
        }
        return now;

    }

    public static int[] mergeArrays(int[] a1, int[] a2) {
        if (a1.length == 0 && a2.length == 0) {
            return new int[]{};
        }
        if (a1.length == 0) {
            return a2;
        }
        if (a2.length == 0) {
            return a1;
        }

        int[] array = new int[a1.length + a2.length];
        int t1 = 0;
        int t2 = 0;
        for (int i = 0; i < array.length; i++) {
            if (a1.length <= t1) {
                array[i] = a2[t2++];
                continue;
            }
            if (a2.length <= t2) {
                array[i] = a1[t1++];
                continue;
            }

            if (a1[t1] >= a2[t2]) {
                array[i] = a2[t2++];
            } else {
                array[i] = a1[t1++];
            }
        }
        return array;
    }

    public static BigInteger factorial(int value) {
        BigInteger bigInteger = new BigInteger(String.valueOf(1));
        for (int i = 2; i <= value; i++) {
            bigInteger = bigInteger.multiply(BigInteger.valueOf(i));
        }
        return bigInteger;
    }

    public static void checkPalindrome(String s) {
        StringBuilder str = new StringBuilder();
        for (int i = 0; i < s.length(); i++) {
            if (Character.isAlphabetic(s.charAt(i)) || Character.isDigit(s.charAt(i))) {
                str.append(Character.toLowerCase(s.charAt(i)));
            }
        }
        for (int i = 0; i < str.length() / 2; i++) {
            if (str.charAt(i) != str.charAt(str.length() - i - 1)) {
                System.out.println("no");
                return;
            }
        }
        System.out.println("yes");
    }

    public static void checkSortArrayLength(int[] array) {
        int cnt = 1;
        int max = 1;
        for (int i = 0; i < array.length - 1; i++) {
            if (array[i + 1] >= array[i]) {
                cnt++;
            } else {
                cnt = 0;
            }
            if (cnt > max) {
                max = cnt;
            }
        }
        System.out.println(max);
    }

    public static boolean isPowerOfTwo(long value) {
        if (value <= 0) {
            return false;
        }
        return (value & (value) - 1) == 0;
    }

    public static boolean isPrime(int k) {
        if (k % 2 == 0) {
            return false;
        }
        for (int i = 3; i <= Math.sqrt(k); i += 2) {
            if (k % i == 0) {
                return false;
            }
        }
        return true;
    }

    public static int fact(int a) {
        int s = 1;
        for (int i = 2; i <= a; i++) {
            s *= i;
        }
        return s;
    }

    public static void selectionSort(int[] arr) {
        for (int i = 0; i < arr.length - 1; i++) {
            int index = i;
            for (int j = i + 1; j < arr.length; j++) {
                if (arr[j] < arr[index]) {
                    index = j;
                }
            }
            swap(arr, index, i);
        }
    }

    public static void swap(int[] array, int i, int j) {
        int temp = array[i];
        array[i] = array[j];
        array[j] = temp;
    }

    public static void swap(int[][] array, int i, int j) {
        int[] temp = array[i];
        array[i] = array[j];
        array[j] = temp;
    }

}