Tak and Hotels

AtCoder

IDarc060_c

Time3000ms

Memory256MB

Difficulty—

$N$ hotels are located on a straight line. The coordinate of the $i$\-th hotel $(1 \leq i \leq N)$ is $x_i$. Tak the traveler has the following two personal principles: * He never travels a distance of more than $L$ in a single day. * He never sleeps in the open. That is, he must stay at a hotel at the end of a day. You are given $Q$ queries. The $j$\-th $(1 \leq j \leq Q)$ query is described by two distinct integers $a_j$ and $b_j$. For each query, find the minimum number of days that Tak needs to travel from the $a_j$\-th hotel to the $b_j$\-th hotel following his principles. It is guaranteed that he can always travel from the $a_j$\-th hotel to the $b_j$\-th hotel, in any given input. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq L \leq 10^9$ * $1 \leq Q \leq 10^5$ * $1 \leq x_i < x_2 < ... < x_N \leq 10^9$ * $x_{i+1} - x_i \leq L$ * $1 \leq a_j,b_j \leq N$ * $a_j \neq b_j$ * $N,\,L,\,Q,\,x_i,\,a_j,\,b_j$ are integers. ## Input The input is given from Standard Input in the following format: $N$ $x_1$ $x_2$ $...$ $x_N$ $L$ $Q$ $a_1$ $b_1$ $a_2$ $b_2$ : $a_Q$ $b_Q$ ## Partial Score * $200$ points will be awarded for passing the test set satisfying $N \leq 10^3$ and $Q \leq 10^3$. [samples]

Samples

Input #1

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5

Output #1

4
2
1
2

For the $1$\-st query, he can travel from the $1$\-st hotel to the $8$\-th hotel in $4$ days, as follows:

*   Day $1$: Travel from the $1$\-st hotel to the $2$\-nd hotel. The distance traveled is $2$.
*   Day $2$: Travel from the $2$\-nd hotel to the $4$\-th hotel. The distance traveled is $10$.
*   Day $3$: Travel from the $4$\-th hotel to the $7$\-th hotel. The distance traveled is $6$.
*   Day $4$: Travel from the $7$\-th hotel to the $8$\-th hotel. The distance traveled is $10$.

API Response (JSON)

{
  "problem": {
    "name": "Tak and Hotels",
    "description": {
      "content": "$N$ hotels are located on a straight line. The coordinate of the $i$\\-th hotel $(1 \\leq i \\leq N)$ is $x_i$. Tak the traveler has the following two personal principles: *   He never travels a distanc",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc060_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$N$ hotels are located on a straight line. The coordinate of the $i$\\-th hotel $(1 \\leq i \\leq N)$ is $x_i$.\nTak the traveler has the following two personal principles:\n\n*   He never travels a distanc...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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