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=[int(i)for i in raw_input().split()]
L=[int(i)for i in raw_input().split()]
L=[(L[i]-L[i+1])/d+1 for i in range(n-1)]
s=0
for i in range(n-2):
        if L[i]>0:
                s+=L[i]
                L[i+1]+=L[i]
if L[n-2]>0:
        s+=L[n-2]
print s