AB Game

AtCoder

IDarc145_b

Time2000ms

Memory256MB

Difficulty—

The following game is called Game $n$: > The game is played by Alice and Bob. Initially, there are $n$ stones. > The players alternate turns, making a move described below, with Alice going first. The player who becomes unable to make a move loses. > > * In Alice's turn, she must remove a number of stones that is a positive multiple of $A$. > * In Bob's turn, he must remove a number of stones that is a positive multiple of $B$. In how many of Game $1$, Game $2$, ..., Game $N$ does Alice win when both players play optimally? ## Constraints * $1 \leq N ,A,B \leq 10^{18}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A$ $B$ [samples]

Samples

Input #1

4 2 1

Output #1

2

In Game $1$, Alice cannot make a move and thus loses.
In Game $2$, Alice removes $2$ stones, and then Bob cannot make a move: Alice wins.
In Game $3$, Alice removes $2$ stones, Bob removes $1$ stone, and then Alice cannot make a move and loses.
In Game $4$, Alice removes $2 \times 2 = 4$ stones, and then Bob cannot make a move: Alice wins.
Therefore, Alice wins in two of the four games.

Input #2

27182818284 59045 23356

Output #2

10752495144

API Response (JSON)

{
  "problem": {
    "name": "AB Game",
    "description": {
      "content": "The following game is called Game $n$: > The game is played by Alice and Bob. Initially, there are $n$ stones. > The players alternate turns, making a move described below, with Alice going first. Th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc145_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The following game is called Game $n$:\n\n> The game is played by Alice and Bob. Initially, there are $n$ stones.\n> The players alternate turns, making a move described below, with Alice going first. Th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments