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

l=list(map(int,input().split()))
n=l[0]
d=l[1]
a=[0]*n
c=0
ans=0
l=input()
l=list(map(int,l.split()))
for i in range(0,n):
    a[i]=int(l[i])
    if i == 0:
        continue
    if a[i] <= a[i-1]:
        c=math.ceil((a[i-1]-a[i])/d)
        if c*d == a[i-1] - a[i]:
            c=c+1
        if c == 0:
            c=1
        elif a[i] == 0:
            c=c+1
        a[i]=a[i]+d*c
        ans=ans+c
        c=0
        
print(ans)