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.

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}.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分