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
val = input().split()
cln = input().split()

ans = 0
tmp = 0

for x in range(0,len(cln)):
	xl = int(cln[x])
	if(xl <= tmp):
		n = tmp - xl
		n = n // int(val[1])
		n = n + 1
		ans = ans + n
		xl = xl + (n * int(val[1]))
			
	tmp = xl

print(ans)