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AtCoder

IDabc109_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ cities on a number line. The $i$\-th city is located at coordinate $x_i$. Your objective is to visit all these cities at least once. In order to do so, you will first set a positive integer $D$. Then, you will depart from coordinate $X$ and perform Move $1$ and Move $2$ below, as many times as you like: * Move $1$: travel from coordinate $y$ to coordinate $y + D$. * Move $2$: travel from coordinate $y$ to coordinate $y - D$. Find the maximum value of $D$ that enables you to visit all the cities. Here, to visit a city is to travel to the coordinate where that city is located. ## Constraints * All values in input are integers. * $1 \leq N \leq 10^5$ * $1 \leq X \leq 10^9$ * $1 \leq x_i \leq 10^9$ * $x_i$ are all different. * $x_1, x_2, ..., x_N \neq X$ ## Input Input is given from Standard Input in the following format: $N$ $X$ $x_1$ $x_2$ $...$ $x_N$ [samples]

Samples

Input #1

3 3
1 7 11

Output #1

2

Setting $D = 2$ enables you to visit all the cities as follows, and this is the maximum value of such $D$.

*   Perform Move $2$ to travel to coordinate $1$.
*   Perform Move $1$ to travel to coordinate $3$.
*   Perform Move $1$ to travel to coordinate $5$.
*   Perform Move $1$ to travel to coordinate $7$.
*   Perform Move $1$ to travel to coordinate $9$.
*   Perform Move $1$ to travel to coordinate $11$.

Input #2

3 81
33 105 57

Output #2

Input #3

1 1
1000000000

Output #3

999999999

API Response (JSON)

{
  "problem": {
    "name": "Skip",
    "description": {
      "content": "There are $N$ cities on a number line. The $i$\\-th city is located at coordinate $x_i$. Your objective is to visit all these cities at least once. In order to do so, you will first set a positive inte",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc109_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ cities on a number line. The $i$\\-th city is located at coordinate $x_i$.\nYour objective is to visit all these cities at least once.\nIn order to do so, you will first set a positive inte...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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