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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
typedef long long ll;

long long min(long long A,long long B){
    return A<B?A:B;
}

int main(void){
    ll n,d,sum=0;
    scanf("%lld%lld",&n,&d);
    ll a[n];
    for (int i=0; i<n; i++){
        scanf("%lld",&a[i]);
        sum+=a[i];
    }
    ll ans=sum*2-a[0]-a[n-1]+d*(n-1);
    for (int i=0; i<n; i++){
        ll tmp=i*(i+1)/2+(n-i-1)*(n-i)/2;
        ans=min(tmp*d+sum-a[i]+a[i]*(n-1),ans);
    }
    printf("%lld\n",ans);
    return 0;
}