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
a=[int(i) for i in input().split()]
b=[int(i) for i in input().split()]
c=a[-1]
n=0
for i in range(len(b)-1):
	if b[i]>b[i+1]:
		d=math.ceil((b[i]-b[i+1])/c)
		n+=d
		b[i+1]+=d*c
	if b[i]==b[i+1]:
		d=1
		n+=1
		b[i+1]+=c
print(n)
