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
from math import *
n,k=map(int,input().split())
l=list(map(int,input().split()))
c=0
for i in range(n-1):
    if(l[i]>l[i+1]):
        d=abs(l[i+1]-l[i])+1
        x=ceil(d/k)
        c=c+x
        l[i+1]=l[i+1]+(x*k)
    elif(l[i]==l[i+1]):
        c+=1
        l[i+1]=l[i]+k
print(c)
