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
def q11a():
	n, d = tuple([int(num) for num in input().split()])
	num_list = [int(num) for num in input().split()]
	count = 0
	for i in range(1, len(num_list)):
		if(num_list[i] <= num_list[i-1]):
			multiple = (num_list[i-1] - num_list[i])//d + 1
			count += multiple
			num_list[i] += d * multiple
	print(count)

q11a()