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
nd=input().split()
n=int(nd[0])
d=int(nd[1])
L=list(map(int,input().split()))
count=0
for i in range(0,len(L)-1):
	if(L[i+1]>L[i]):
		count+=0
	elif(L[i+1]==L[i]):
		count+=1
		L[i+1]+=d
	else:
		z=(L[i]-L[i+1])/d
		if(int(z)!=z):
			z=math.ceil(z)
			
		else:
			z=int(z)+1
		count+=z
		L[i+1]+=z*d
		
	#print(count)
print(count)
#print(L)