±AB

AtCoder

IDarc127_f

Time8000ms

Memory256MB

Difficulty—

Given are integers $A$, $B$, $V$, and $M$, where $A$ and $B$ are guaranteed to be coprime. Additionally, you have an integer $x$. Initially, $x=V$. You can do the following four kinds of operations any number of times in any order. * Replace the value of $x$ with $x+A$. * Replace the value of $x$ with $x-A$. * Replace the value of $x$ with $x+B$. * Replace the value of $x$ with $x-B$. Here, $0 \leq x \leq M$ must hold at any moment during this process. Under this condition, find how many different values $x$ can take. For each input file, solve $T$ test cases. ## Constraints * $1 \leq T \leq 10^5$ * $1 \leq A < B \leq M \leq 10^9$ * $A$ and $B$ are coprime. * $0 \leq V \leq M$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $T$ $case_1$ $case_2$ $\vdots$ $case_3$ Each case is in the following format: $A$ $B$ $V$ $M$ [samples]

Samples

Input #1

5
3 5 0 5
1 2 5 10
5 8 4 9
10 99 48 106
500000000 500000001 123456789 900000000

Output #1

4
11
4
10
800000002

In the first case, $x$ can take four values: $x=0,2,3,5$.

API Response (JSON)

{
  "problem": {
    "name": "±AB",
    "description": {
      "content": "Given are integers $A$, $B$, $V$, and $M$, where $A$ and $B$ are guaranteed to be coprime. Additionally, you have an integer $x$. Initially, $x=V$. You can do the following four kinds of operations an",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 8000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc127_f"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are integers $A$, $B$, $V$, and $M$, where $A$ and $B$ are guaranteed to be coprime. Additionally, you have an integer $x$. Initially, $x=V$.\nYou can do the following four kinds of operations an...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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