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(x) for x in input().split(" ")]
l=[int(x) for x in input().split(" ")]
m=0
for i in range(1,len(l)):
    if l[i]<=l[i-1]:
        a=l[i-1]-l[i]+1
        if a%d==0:
            m+=a//d
            l[i]+=a
        else:
            m+=(a//d)+1
            l[i]+=d*((a//d)+1)
print(m)        