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
s=raw_input().split()
n=int(s[0])
d=int(s[1])
A=[int(x) for x in raw_input().split()]
r=0
for i in range(1,n):
	if A[i-1]>=A[i]:
		k=(A[i-1]-A[i])/d+1
		A[i]+=k*d
		r+=k
print r
