Connecting Cities

AtCoder

IDkeyence2019_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ cities in Republic of AtCoder. The size of the $i$\-th city is $A_{i}$. Takahashi would like to build $N-1$ bidirectional roads connecting two cities so that any city can be reached from any other city by using these roads. Assume that the cost of building a road connecting the $i$\-th city and the $j$\-th city is $|i-j| \times D + A_{i} + A_{j}$. For Takahashi, find the minimum possible total cost to achieve the objective. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq D \leq 10^9$ * $1 \leq A_{i} \leq 10^9$ * $A_{i}$ and $D$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $D$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

3 1
1 100 1

Output #1

106

This cost can be achieved by, for example, building roads connecting City $1$, $2$ and City $1$, $3$.

Input #2

3 1000
1 100 1

Output #2

Input #3

6 14
25 171 7 1 17 162

Output #3

Input #4

12 5
43 94 27 3 69 99 56 25 8 15 46 8

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Connecting Cities",
    "description": {
      "content": "There are $N$ cities in Republic of AtCoder. The size of the $i$\\-th city is $A_{i}$. Takahashi would like to build $N-1$ bidirectional roads connecting two cities so that any city can be reached from",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "keyence2019_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ cities in Republic of AtCoder. The size of the $i$\\-th city is $A_{i}$. Takahashi would like to build $N-1$ bidirectional roads connecting two cities so that any city can be reached from...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments