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 yourself 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:
 - $1 \le m \le 1000$: the total number of people who entered the lottery.
 - $1 \le n \le m$: the total number of winners drawn.
 - $1 \le t \le 100$: the number of tickets each winner is allowed to buy.
 - $1 \le p \le m$: 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 $10^{-9}$.

-----Examples-----
Sample Input 1:
100 10 2 1
Sample Output 1:
0.1

Sample Input 2:
100 10 2 2
Sample Output 2:
0.1909090909

Difficulty: competition

Starter code:

Solutions: