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
##codeforces 11A
import math
def secuencia(lista,d):
    cont=0
    for i in range(len(lista)-1):
        if lista[i]>=lista[i+1]:
           n=math.floor((lista[i]-lista[i+1])/d)+1
           lista[i+1]=lista[i+1]+n*d
           cont+=n
    return cont

ll,d = map(int, input().split(' '))
l = list(map(int, input().split(' ')))

print(secuencia(l,d))