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Contest: Task: Related: TaskB

Score : $100$ points

Problem Statement

In a certain programming contest, T-shirts are awarded to participants according to the following rules.

  • All participants who ranked $A$-th or higher get a T-shirt.
  • Additionally, from the participants who ranked between $(A+1)$-th and $B$-th (inclusive), $C$ participants chosen uniformly at random get a T-shirt.

There were $1000$ participants in this contest, and all of them got different ranks.
Iroha-chan, who participated in this contest, ranked $X$-th.
Find the probability that she gets a T-shirt.

Constraints

  • All values in input are integers.
  • $1 \le A < B \le 1000$
  • $1 \le C \le B-A$
  • $1 \le X \le 1000$

Input

Input is given from Standard Input in the following format:

$A$ $B$ $C$ $X$

Output

Print the answer. Your output will be considered correct if the absolute or relative error from the judge's answer is at most $10^{−6}$.

Sample Input 1

30 500 20 103

Sample Output 1

0.042553191489

Iroha-chan ranked $103$-rd.
She will get a T-shirt if she is among the $20$ participants chosen uniformly at random from the $470$ participants who ranked between $31$-st and $500$-th, which happens with probability $\frac{20}{470}=0.04255319\dots$.

Sample Input 2

50 500 100 1

Sample Output 2

1.000000000000

Iroha-chan ranked $1$-st. This time, she is guaranteed to get a T-shirt.

Sample Input 3

1 2 1 1000

Sample Output 3

0.000000000000

Iroha-chan ranked $1000$-th. This time, she will never get a T-shirt.