human
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
Using python3 can you solve the prior task?
assistant
#Here is the least number of moves required to make the given sequence increasing.

import itertools
import math

import time
def timer(f):
    def tmp(*args, **kwargs):
        t = time.time()
        res = f(*args, **kwargs)
        print("Время выполнения функции: %f" % (time.time()-t))
        return res

    return tmp

#n = int(input())

n, d = map(int, input().split(' '))
array = list(map(int, input().split(' ')))
total = 0
for i in range(1, len(array)):
    if array[i]<=array[i-1]:
        dif = array[i-1]-array[i]+1
        q = math.ceil(dif/d)
        array[i]+=d*q
        total+=q
print(total)