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 Tue Dec 19 16:55:13 2017

@author: талгат
"""

l=lambda:map(int, raw_input().split())
n,d=l()
c=l()
r=0
for i in range(1,n):
    D=c[i-1]-c[i]
    if D >= 0:
        R=-~(D/d)
        c[i] += R*d
        r+=R
print r