[SNCPC2019] K-hour Clock

Luogu

IDLGP9645

Time1000ms

Memory256MB

DifficultyP1

数学2019Special JudgeO2优化陕西省赛/邀请赛

A $k$-hour clock is a day keeping method which follows the rules below: - A day is divided into $k$ hours, where the $i$-th hour is called the $(i-1)$ o' clock; - If it's $x$ o'clock now, it will be $(x+1)$ o'clock after $1$ hour if $0 \le x < k - 1$; - If it's $(k - 1)$ o'clock now, it will be $0$ o'clock after $1$ hour. We know that it's $x$ o'clock now, and after $y$ hours it will be $z$ o'clock. What's the value of $k$? ## Input There are multiple test cases. The first line of the input is an integer $T$ (about $10^5$), indicating the number of test cases. For each test case: The first and only line contains three integers $x$, $y$ and $z$ ($0 \le x, z \le 10^9$, $1 \le y \le 10^9$). ## Output For each test case output one line containing one integer, indicating the value of $k$. Note that there must be $1 \le k \le 2 \times 10^9$. If there are multiple valid answers, you can print any of them; If there is no valid answer, print ``-1`` (without quotes) instead. [samples]

Samples

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API Response (JSON)

{
  "problem": {
    "name": "[SNCPC2019] K-hour Clock",
    "description": {
      "content": "A $k$-hour clock is a day keeping method which follows the rules below: - A day is divided into $k$ hours, where the $i$-th hour is called the $(i-1)$ o' clock; - If it's $x$ o'clock now, it will be ",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
    },
    "difficulty": {
      "LuoguStyle": "P1"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9645"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "A $k$-hour clock is a day keeping method which follows the rules below:\n\n- A day is divided into $k$ hours, where the $i$-th hour is called the $(i-1)$ o' clock;\n- If it's $x$ o'clock now, it will be ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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