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 -*-
import sys

def some_func():
    """
    """
    count = 0
    n,m = map(int, raw_input().split(' '))
    n_list = map(int, raw_input().split(' '))

    for i in range(1,n):
        temp = 0
        if n_list[i] > n_list[i-1]:
            pass
        else:
            temp = (n_list[i-1]-n_list[i])/m
            if n_list[i] + temp*m > n_list[i-1]:
                count+=temp
                n_list[i] += temp*m
            else:
                count+=(temp+1)
                n_list[i] += (temp+1)*m
    print count

if __name__ == '__main__':
  some_func()



