Problem:
Score : 600 points

Problem Statement

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

Output

Print the minimum possible total cost.

Sample Input 1

3 1
1 100 1

Sample Output 1

106

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

Sample Input 2

3 1000
1 100 1

Sample Output 2

2202

Sample Input 3

6 14
25 171 7 1 17 162

Sample Output 3

497

Sample Input 4

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

Sample Output 4

658

Solution in Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.collection.mutable.ListBuffer

object Main {
  def main(args: Array[String]): Unit = {
    println(func())
  }

  def func() : Long = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    val d = sc.nextLong
    val cities = List.fill(n)(sc.nextLong).zipWithIndex

    var costs:ListBuffer[Long] = ListBuffer.empty

    cities.foreach{case(x,i) => {
      costs += cities.map{case (y,j) =>
        (i-j).abs*d+x+y
      }.min
    }}

    val max = costs.max

    costs.sum - max
  }
}