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 main():
	(n, d) = input().split()
	d = int(d)
	l = input().split()
	l = [int(x) for x in l]
	print(solver(l, d))

def solver(l, d):
	assert(len(l) >= 2)
	total = 0
	current = l[0]
	for x in l[1:]:
		if x <= current:
			ds = (current - x) // d + 1
			total += ds
			x += ds * d
		current = x
	return total

main()
#print(solver([1, 3, 3, 2, 1], 3))



