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
k=input().split()
n=int(k[0])
d=int(k[1])
c=0
a = list(map(int, input().rstrip().split()))
b=a[0]
for i in range(1,n):
  if a[i]<=b:
    x=(b-a[i])//d+1
    c+=x
    b=a[i]+x*d
  else:
    b=a[i]
print(c)
   
	 	 		       	  	   	 		     		