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
y=lambda x:[int(i) for i in x]
 
n,d=y(input().split())
 
sequence=y(input().split())
 
x=0
 
for i in range(n):
    if i:
        if sequence[i]<=sequence[i-1]:
            num=((sequence[i-1]-sequence[i])//d)+1
            sequence[i]+=num*d
            x+=num
        
print(x)
