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
s=raw_input()
l=s.split(' ')
n=int(l[0]); d=int(l[1])
s=raw_input()
l=s.split(' ')
l=[int(i) for i in l]
#print l
ans=0
for i in range(1, n):
    if l[i]>l[i-1]: continue
    t=(l[i-1]-l[i])/d + 1
    ans+=t
    #print ans
    l[i]+=t*d

    
print ans
