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
n,d=map(int,raw_input().split())
a=map(int,raw_input().split())
c=0
#for i in range (0, n, 1):
#	x=int(input())
#	a.append(x)
for i in range (1, n, 1):
	if a[i]<=a[i-1]:
		temp=a[i-1]-a[i]
		a[i]+=(temp/d)*d+d
		c+=(temp/d)+1
print(c)
