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: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=2e5+7;
int n,fa[N];
ll ans,d,a[N],l[N],r[N];
int main()
{
	cin>>n>>d;
	ans=(n-1)*d;
	for(int i=1;i<=n;i++)scanf("%lld",&a[i]),ans+=a[i],l[i]=r[i]=1e18;
	l[1]=a[1];
	for(int i=2;i<=n;i++)l[i]=min(l[i-1],a[i]-(i-1)*d);
	r[n]=a[n]+(n-1)*d;
	for(int i=n-1;i;i--)r[i]=min(r[i+1],a[i]+(i-1)*d);
	for(int i=2;i<n;i++)ans+=min((i-1)*d+l[i],r[i]-(i-1)*d);
	cout<<ans<<endl;
}