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 mc(v,d,n):
	"""get move count"""
	r=0
	for c in range(n-1):
		vd=v[c]-v[c+1]
		cr=(vd//d+1) if vd>=0 else 0
		v[c+1]+=cr*d
		r+=cr
	return r

n,d=[int(c) for c in input().split()]
v=[int(c) for c in input().split()]
print(mc(v,d,n))