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,input().split())
a=list(map(int,input().split()))
c=0

for i in range(len(a)-1):
	if(a[i+1]<=a[i]):
		if((a[i]-a[i+1])<d):
			a[i+1]=a[i+1]+d
			c=c+1
		else:
			x=int(math.ceil((a[i]-a[i+1])/d))
			a[i+1]=a[i+1]+x*d
			c=c+x
		if(a[i+1]==a[i]):
			a[i+1]=a[i+1]+d
			c=c+1
print(c)