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,m=map(int,raw_input().split())
a=map(int,raw_input().split())
pre=-1
ans=0
for x in a:
    if pre==-1:
        pre=x
    else:
        while x<=pre:
            diff=pre-x;
            if diff<m:
                ans=ans+1
                x=x+m
                continue
            cnt=diff/m
            ans=ans+cnt
            x=x+cnt*m
        pre=x
print ans