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())
li=list(map(int,input().split()))
count=0
for i in range(1,n):
	if li[i-1]>li[i]:
		j=li[i-1]-li[i]
		f=j/d
		k=j//d
		if f>=1:
			li[i]+=(k+1)*d
			count+=(k+1)
		else:
			li[i]+=d
			count+=1
	elif li[i-1]==li[i]:
		count+=1
		li[i]+=d
print(count)