T-shirt

AtCoder

IDabc242_a

Time2000ms

Memory256MB

Difficulty—

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: $A$ $B$ $C$ $X$ [samples]

Samples

Input #1

30 500 20 103

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 $\frac{20}{470}=0.04255319\dots$.

Input #2

50 500 100 1

Output #2

1.000000000000

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

Input #3

1 2 1 1000

Output #3

0.000000000000

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

API Response (JSON)

{
  "problem": {
    "name": "T-shirt",
    "description": {
      "content": "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 pa",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc242_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In a certain programming contest, T-shirts are awarded to participants according to the following rules.\n\n*   All participants who ranked $A$\\-th or higher get a T-shirt.\n*   Additionally, from the pa...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments