Training

AtCoder

IDarc123_e

Time3000ms

Memory256MB

Difficulty—

Two programmers, $X$ and $Y$, are going to start competitive programming. One's skill in competitive programming is represented by a positive integer called the _level_. Initially, $X$'s level is $A_X$, and $Y$'s level is $A_Y$. The two will do learning tasks to raise their levels. We know that they level up as follows. * $X$'s level raises by one after every $B_X$ learning tasks. * $Y$'s level raises by one after every $B_Y$ learning tasks. How many among $n = 1, 2, \ldots, N$ satisfy the following? * $X$'s level and $Y$'s level are equal when each of them has done exactly $n$ learning tasks. Process $T$ test cases per input file. ## Constraints * $1\leq T\leq 2\times 10^5$ * $1\leq N\leq 10^{9}$ * $1\leq A_X, B_X, A_Y, B_Y \leq 10^6$ ## Input Input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\text{case}_2$ $\vdots$ $\text{case}_T$ Each case is in the following format: $N$ $A_X$ $B_X$ $A_Y$ $B_Y$ [samples]

Samples

Input #1

5
10 5 3 4 2
5 5 3 4 2
100 5 3 4 2
10 5 3 4 3
10 5 10 5 9

Output #1

6
3
6
0
9

We will describe the first test case.
For each $n = 1, 2, \ldots, 10$, the two's levels after doing $n$ learning tasks are as follows.

*   $X$'s level: $5, 5, 6, 6, 6, 7, 7, 7, 8, 8$.
*   $Y$'s level: $4, 5, 5, 6, 6, 7, 7, 8, 8, 9$.

There are six scenarios ($n = 2, 4, 5, 6, 7, 9$) where the two's levels are equal, so the answer is $6$.

API Response (JSON)

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      "content": "Two programmers, $X$ and $Y$, are going to start competitive programming. One's skill in competitive programming is represented by a positive integer called the _level_. Initially, $X$'s level is $A_X",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc123_e"
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  "statements": [
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      "statement_type": "Markdown",
      "content": "Two programmers, $X$ and $Y$, are going to start competitive programming.\nOne's skill in competitive programming is represented by a positive integer called the _level_. Initially, $X$'s level is $A_X...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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