README

Ticket Lottery 
Problem ID: lottery

You and your friends are in New York and are planning to go see a Broadway musical. 
Unfortunately, New York being New York, the tickets are just a tiny bit expensive. 
But one of the shows has a ticket lottery each night where impecunious people such 
as you have a chance to win the right to buy slightly less expensive tickets to 
good seats. The lottery operates as follows. First, everyone interested enters the 
lottery. Then, n lucky winners are drawn, and each of these is offered to buy up to
t tickets. 

Given the number of people p in your group (all of which entered the 
lottery) and the total number of people m that entered the lottery, what is the 
probability that you will be able to get tickets for your entire group? Assume that 
the n lucky winners are chosen uniformly at random from the m people that entered 
the lottery, and that each person can win at most once.

Input:
The input consists of a single line containing four integers:
1 <= m <= 1000: the total number of people who entered the lottery. 
1 <= n <= m: the total number of winners drawn. 
1 <= t <= 100: the number of tickets each winner is allowed to buy. 
1 <= p <= m: the number of people in your group.

Output:
Output a single line containing the probability that your entire group can get 
tickets to the show. This probability should be given with an absolute error of at
most 10^-9.

Sample input 1, 100 10 2 1 - Sample output 1, 0.1 
Sample input 2, 100 10 2 2 - Sample output 2, 0.1909090909 
Sample input 3, 10 10 5 1  - Sample output 3, 1.0000000000