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,k=map(int,input().split())
l=list(map(int,input().split()))
count=0
for x in range(n-1):
	if l[x+1]<l[x]:
		q=abs(l[x+1]-l[x])//k 
		count+=(q)
		l[x+1]+=k*q
		if l[x+1]<=l[x]:
			l[x+1]+=k
			count+=1
	elif l[x+1]==l[x]:
		l[x+1]+=k
		count+=1
print(count)