Bridge and Sheets

AtCoder

IDarc134_a

Time2000ms

Memory256MB

Difficulty—

Snuke bought a bridge of length $L$. He decided to cover this bridge with blue tarps of length $W$ each. Below, a position on the bridge is represented by the distance from the left end of the bridge. When a tarp is placed so that its left end is at the position $x$ ($0 \leq x \leq L-W$, $x$ is real), it covers the range $[x, x+W]$. (Note that both ends are included.) He has already placed $N$ tarps. The left end of the $i$\-th tarp is at the position $a_i$. At least how many more tarps are needed to cover the bridge entirely? Here, the bridge is said to be covered entirely when, for any real number $x$ between $0$ and $L$ (inclusive), there is a tarp that covers the position $x$. ## Constraints * All values in input are integers. * $1 \leq N \leq 10^{5}$ * $1 \leq W \leq L \leq 10^{18}$ * $0 \leq a_1 < a_2 < \cdots < a_N \leq L-W$ ## Input Input is given from Standard Input in the following format: $N$ $L$ $W$ $a_1$ $\cdots$ $a_N$ [samples]

Samples

Input #1

2 10 3
3 5

Output #1

2

*   The bridge will be covered entirely by, for example, placing two tarps so that their left ends are at the positions $0$ and $7$.

Input #2

5 10 3
0 1 4 6 7

Output #2

Input #3

12 1000000000 5
18501490 45193578 51176297 126259763 132941437 180230259 401450156 585843095 614520250 622477699 657221699 896711402

Output #3

199999992

API Response (JSON)

{
  "problem": {
    "name": "Bridge and Sheets",
    "description": {
      "content": "Snuke bought a bridge of length $L$. He decided to cover this bridge with blue tarps of length $W$ each. Below, a position on the bridge is represented by the distance from the left end of the bridge.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc134_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke bought a bridge of length $L$. He decided to cover this bridge with blue tarps of length $W$ each.\nBelow, a position on the bridge is represented by the distance from the left end of the bridge....",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments