A sequence a0, a1, ..., at - 1 is called increasing if ai - 1 < ai for each i: 0 < i < t.

You are given a sequence b0, b1, ..., bn - 1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?

Input

The first line of the input contains two integer numbers n and d (2 ≤ n ≤ 2000, 1 ≤ d ≤ 106). The second line contains space separated sequence b0, b1, ..., bn - 1 (1 ≤ bi ≤ 106).

Output

Output the minimal number of moves needed to make the sequence increasing.

Examples

Input

4 2
1 3 3 2


Output

3
import math
def getNrOfOperations():
       #n is the number of terms in sequence
       #d is the number to be added to elements in order to make increasing sequence
       n,d =map(int,input().strip().split())

       #get the sequence from input and make it to be a list
       sequence = list(map(int,input().strip().split()))

       count = 0

       for termIndex in range(n-1):
              # if next term is smaller than previous
              if sequence[termIndex+1] < sequence[termIndex]:
                     #add nr of operations 
                     count += math.ceil((sequence[termIndex]-sequence[termIndex+1])/d)
                     #give new value to next term
                     sequence[termIndex+1] += math.ceil((sequence[termIndex]-sequence[termIndex+1])/d)*d
              # if next term is equal to previous
              if sequence[termIndex+1] == sequence[termIndex]:
                     #nr of operations is 1
                     count += 1
                     sequence[termIndex+1] += d
       return count    
print(getNrOfOperations())