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
# -*- coding: utf-8 -*-
"""
Created on Mon Apr 24 18:38:07 2017

@author: wb
"""

n,d=map(int,raw_input().split())
list=map(int,raw_input().split())

ans=0
for i in range(1,len(list)):
    if list[i-1]>=list[i]:
        x=(list[i-1]-list[i])/d
        list[i]=list[i]+x*d+d
        ans=ans+x+1
    
print(ans)