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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main()
{
	int n,d;
	cin >> n >> d;
	int a[n];
	for(int i = 0; i < n; i++)
		cin >> a[i];

	long long ans = -1;
	for(int i = 1; i < n; i++){
		long long cost = i * d + a[0] + a[i];
		for(int j = 1; j < n; j++){
			if(j != i){
				int costAdd = abs(i - j) * d + a[i] + a[j];
				for(int k = 0; k < j; k++){
					costAdd = min(costAdd, abs(k - j) * d + a[k] + a[j]);
				}
				cost += costAdd;
			}
		}
		if(ans == -1 || ans > cost)
			ans = cost;
	}

	cout << ans << "\n";

	return 0;
}