Problem: Maxim has opened his own restaurant! The restaurant has got a huge table, the table's length is p meters.

Maxim has got a dinner party tonight, n guests will come to him. Let's index the guests of Maxim's restaurant from 1 to n. Maxim knows the sizes of all guests that are going to come to him. The i-th guest's size (ai) represents the number of meters the guest is going to take up if he sits at the restaurant table.

Long before the dinner, the guests line up in a queue in front of the restaurant in some order. Then Maxim lets the guests in, one by one. Maxim stops letting the guests in when there is no place at the restaurant table for another guest in the queue. There is no place at the restaurant table for another guest in the queue, if the sum of sizes of all guests in the restaurant plus the size of this guest from the queue is larger than p. In this case, not to offend the guest who has no place at the table, Maxim doesn't let any other guest in the restaurant, even if one of the following guests in the queue would have fit in at the table.

Maxim is now wondering, what is the average number of visitors who have come to the restaurant for all possible n! orders of guests in the queue. Help Maxim, calculate this number.

Input

The first line contains integer n (1 ≤ n ≤ 50) — the number of guests in the restaurant. The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 50) — the guests' sizes in meters. The third line contains integer p (1 ≤ p ≤ 50) — the table's length in meters. 

The numbers in the lines are separated by single spaces.

Output

In a single line print a real number — the answer to the problem. The answer will be considered correct, if the absolute or relative error doesn't exceed 10 - 4.

Examples

Input

3
1 2 3
3


Output

1.3333333333

Note

In the first sample the people will come in the following orders: 

  * (1, 2, 3) — there will be two people in the restaurant; 
  * (1, 3, 2) — there will be one person in the restaurant; 
  * (2, 1, 3) — there will be two people in the restaurant; 
  * (2, 3, 1) — there will be one person in the restaurant; 
  * (3, 1, 2) — there will be one person in the restaurant; 
  * (3, 2, 1) — there will be one person in the restaurant. 



In total we get (2 + 1 + 2 + 1 + 1 + 1) / 6 = 8 / 6 = 1.(3).

Solution (in JAVA):

Solution:

import java.io.*;
import java.math.BigInteger;
import java.util.*;



public class B {
    private static final int mod = (int)1e9+7;

    int n;
    int[] a;
    int p;

    public void run() throws IOException {
        a = new int[n = IOFast.nextInt()];
        for(int i = 0; i < n; i++) {
            a[i] = IOFast.nextInt();
        }
        p = IOFast.nextInt();

        double res = 0;
        int sum = 0;
        for(int i = 0; i < n; i++) {
            sum += a[i];
        }
        if(sum <= p) {
            IOFast.out.printf("%.10f\n", (double)n);
            return;
        }
        
        double[][] dp = new double[51][51];
        for(int i = 0; i < n; i++) {
            for(double[] d : dp) Arrays.fill(d, 0);
            dp[0][0] = 1;
            for(int j = 0, x = 1, y; j < n; j++) if(i != j) {
                x++;
                for(int u = n; u >= 0; u--) {
                    for(int k = p; k >= 0; k--) {
                        if(u < n && k + a[j] <= p) {
                            dp[u + 1][k + a[j]] += dp[u][k] * (u + 1.0) / x;
                        }
                        
                        dp[u][k] *= 1 - (u + 1.0) / x;
                    }
                }
            }
            
            for(int j = 0; j <= n; j++) {
                for(int k = 0; k <= p; k++) if(a[i] + k > p) {
                    res += dp[j][k] * j;
//                  if(dp[j][k] > 0) { System.err.println(i + " " + j + " " + k + ": " + dp[j][k]); }
                }
            }
        }

        IOFast.out.printf("%.10f\n", res);
    }

    public static void main(String[] args) throws IOException {
        //      IOFast.setFileIO("input.txt", "output.txt");
        new B().run();
        IOFast.out.flush();
    }



    static public class IOFast {
        private static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        private static PrintWriter out = new PrintWriter(System.out);

        static void setFileIO(String ins, String outs) throws IOException {
            try {
                in = new BufferedReader(new FileReader(ins));
                out = new PrintWriter(new FileWriter(outs));
            }
            catch(IOException e) {
                System.err.println(e);
                throw e;
            }
        }

        //      private static final int BUFFER_SIZE = 50 * 200000;
        private static int pos, readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static final StringBuilder buf = new StringBuilder();
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];

        static {
            for(int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
        }

        static boolean endInput;

        private static int read() throws IOException {
            if(readLen == -1) {
                return -1;
            }

            if(pos >= readLen) {
                readLen = in.read(buffer);
                pos = 0;

                if(readLen <= 0) {
                    return -1;
                }
            }

            return buffer[pos++];
        }

        private static int nextInt() throws IOException {
            boolean plus = false;
            int ret = 0;
            while(true) {
                final int c = read();

                if(c == -1) {
                    endInput = true;
                    return Integer.MIN_VALUE;
                }

                if(isDigit[c]) {
                    if(c != '-') {
                        plus = true;
                        ret = c - '0';
                    }
                    break;
                }
            }

            while(true) {
                final int c = read();
                if(c == -1 || !isDigit[c]) {
                    break;
                }
                ret = ret * 10 + c - '0';
            }

            return plus ? ret : -ret;
        }

        private static long nextLong() throws IOException {
            boolean plus = false;
            long ret = 0;
            while(true) {
                final int c = read();

                if(c == -1) {
                    endInput = true;
                    return Integer.MIN_VALUE;
                }

                if(isDigit[c]) {
                    if(c != '-') {
                        plus = true;
                        ret = c - '0';
                    }
                    break;
                }
            }

            while(true) {
                final int c = read();
                if(c == -1 || !isDigit[c]) {
                    break;
                }
                ret = ret * 10 + c - '0';
            }

            return plus ? ret : -ret;
        }

        private static char nextChar() throws IOException {
            while(true) {
                final int c = read();

                if(c == -1) {
                    endInput = true;
                    return '\0';
                }

                if(!isSpace[c]) {
                    return (char)c;
                }
            }
        }

        private static String next() throws IOException {
            buf.setLength(0);

            while(true) {
                final int c = read();

                if(c == -1) {
                    endInput = true;
                    return "-1";
                }

                if(!isSpace[c]) {
                    buf.append((char)c);
                    break;
                }
            }

            while(true) {
                final int c = read();

                if(c == -1 || isSpace[c]) {
                    break;
                }
                buf.append((char)c);
            }

            return buf.toString();
        }

        private static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

    }

}