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
notused, step = list(map(int, input().split(" ")))
integers = list(map(int, input().split(" ")))
curr,moves = integers[0],0
for integer in integers[1:]:
	#print(curr, integer, moves)
	if integer <= curr:
		times = (curr - integer)//step + 1
		if times == 0: times +=1
		moves +=times
		curr = integer+ times * step
	else: curr = integer
print(moves)