Score : $100$ points

问题描述

在某次编程竞赛中，T恤衫将根据以下规则颁发给参赛者。

• 所有排名在 $A$ 或更高的参赛者都将获得一件 T 恤。
• 另外，从排名第 $(A+1)$ 到第 $B$（包含）之间的参赛者中，随机均匀选出 $C$ 名参赛者也将获得一件 T 恤。

这次竞赛共有 $1000$ 名参赛者，并且所有人的排名各不相同。
参加了本次比赛的 Iroha-chan 排名在第 $X$ 位。
请计算她获得 T 恤的概率。

以上为通义千问 qwen-max 翻译，仅供参考。

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.

update @ 2024/3/10 10:24:46