The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Maxim and Restaurant

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMaxim 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 (*a*_{i}) 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 *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 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).

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/24/2022 09:32:40 (j1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|