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
y=input().split()
n=int(y[0])
k=int(y[1])
spisok = [int(x) for x in input().split()]
s=0
for i in range(n-1):
	if spisok[i+1] <= spisok[i]:
		r=spisok[i]-spisok[i+1]
		d=(r//k)+1
		spisok[i+1]+=d*k
		s+=d
print(s)