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
import math
n,d=map(int,raw_input().strip().split(" "))
arr=map(float,raw_input().strip().split(" "))
tot=0
for i in range(1,n):
    if(arr[i]<arr[i-1]):
        m=(int)(math.ceil((arr[i-1]-arr[i])/(float)(d)))
        n1,n2=(int)(arr[i]),(int)(arr[i-1])
        if((n2-n1)%d==0):
            m+=1
        tot+=m
        arr[i]=arr[i]+(m*d)
    elif(arr[i]==arr[i-1]):
        tot+=1
        arr[i]=arr[i-1]+d
print tot
            
    
