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
from math import floor
a=input()
s=input()
a1=a.split(" ")
n=int(a1[0])
d=int(a1[1])
s1=list(map(int,s.split(" ")))
c=0
for i in range(1,n):
    r=(s1[i]-s1[i-1])
    if r<=0:
        add=floor(-r/d)+1
        s1[i]+=(add*d)
        c+=add
print(c)