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

line1 = [int(x) for x in raw_input().split()]
line2 = [int(x) for x in raw_input().split()]
count = line1[0]
summer = line1[1]

moves = 0
for x in range(0,count-1):
	if line2[x] >= line2[x+1]:
		moves += ((line2[x]-line2[x+1])/summer) + 1
		line2[x+1] += summer * (((line2[x]-line2[x+1])/summer) + 1)

print moves