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
x=[int(n) for n in input().split()]
s=[int(n) for n in input().split()]
l=0
for n in range(1,x[0]):
	if s[n]==s[n-1]:
		s[n]+=x[1]
		l+=1
	elif s[n]<s[n-1]:
		j=(s[n-1]-s[n]+1)
		if j%x[1]==0:
			k=(s[n-1]-s[n]+1)//x[1]
		else:
			k=1+((s[n-1]-s[n]+1)//x[1])
		
		s[n]+=k*x[1]
	#	print(k*x[1])
		l+=k
print(l)