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
def main():
	nd=map(int,raw_input().split(" "))
	n=nd[0]
	d=nd[1]
	moves=0
	a=map(int,raw_input().split(" "))
	for i in range(len(a)-1):
		if a[i]>=a[i+1]:
			dif=a[i]-a[i+1]
			nom=dif/d;
			nom+=1
			a[i+1]+=d*nom;
			moves+=nom
	print moves
main()