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



n,d = map(int,input().split())



t= list(map(int,input().split()))


import math



p=0
for k in range(n-1):
    if t[k]==t[k+1]:
        p+=1
        t[k+1]+=d
    elif t[k]> t[k+1]:
        if (t[k]-t[k+1])%d==0:
            p+=math.ceil((t[k]-t[k+1])/d)+1
            t[k+1]+=math.ceil((t[k]-t[k+1])/d)*d+d
        else:
            p+=math.ceil((t[k]-t[k+1])/d)
            t[k+1]+=math.ceil((t[k]-t[k+1])/d)*d
    




print(p)
