11_A. Increasing Sequence
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
```python
n,d=map(int,input().split())
l=[int(i) for i in input().split()]
s=0
import math 
for i in range(1,n):
    if l[i]>l[i-1]: 
        continue
    
    diff=l[i-1]-l[i]+1 
    
    s+=math.ceil(diff/d)
    l[i]+=d*math.ceil(diff/d)
print(s)
```