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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

def getR(x):
  if T[x] == x:
    return x
  return getR(T[x])

def judT(x, y):
  xR = getR(x)
  yR = getR(y)
  if xR != yR:
    T[xR] = yR
  return xR != yR

N, D = list(map(int,input().split()))
A = list(map(int, input().split()))

L = [((j-i) * D + A[i] + A[j], i, j) for i in range(N) for j in range(i+1, N)]
 
L.sort()

T = [i for i in range(N)]

C = 0
A = 0

for i in L:
  if judT(i[1], i[2]):
    C += 1
    A += i[0]
    #print(i)
    if C == N-1:
      break
 
print(A)