Count Balls

AtCoder

IDabc158_b

Time2000ms

Memory256MB

Difficulty—

Takahashi has many red balls and blue balls. Now, he will place them in a row. Initially, there is no ball placed. Takahashi, who is very patient, will do the following operation $10^{100}$ times: * Place $A$ blue balls at the end of the row of balls already placed. Then, place $B$ red balls at the end of the row. How many blue balls will be there among the first $N$ balls in the row of balls made this way? ## Constraints * $1 \leq N \leq 10^{18}$ * $A, B \geq 0$ * $0 < A + B \leq 10^{18}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A$ $B$ [samples]

Samples

Input #1

8 3 4

Output #1

4

Let `b` denote a blue ball, and `r` denote a red ball. The first eight balls in the row will be `bbbrrrrb`, among which there are four blue balls.

Input #2

8 0 4

Output #2

0

He placed only red balls from the beginning.

Input #3

6 2 4

Output #3

2

Among `bbrrrr`, there are two blue balls.

API Response (JSON)

{
  "problem": {
    "name": "Count Balls",
    "description": {
      "content": "Takahashi has many red balls and blue balls. Now, he will place them in a row. Initially, there is no ball placed. Takahashi, who is very patient, will do the following operation $10^{100}$ times: * ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc158_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has many red balls and blue balls. Now, he will place them in a row.\nInitially, there is no ball placed.\nTakahashi, who is very patient, will do the following operation $10^{100}$ times:\n\n* ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments