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
n,d=map(int,input().split())
liste=list(map(int,input().split()))
j=0

for i in range(0,len(liste)-1):
    if liste[i]>=liste[i+1]:
        j+=((liste[i]-liste[i+1])//d)+1
        liste[i+1]+=d*((liste[i]-liste[i+1])//d)+d
       
    
print(j)      