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
# your code goes here
n,d = map(int,input().split())
a = list(map(int,input().split()))
ans=0
for i in range(1,len(a)):
	if a[i] <= a[i-1]:
		temp = (a[i-1] - a[i])//d + 1
		ans = ans + temp
		a[i] = a[i] + temp*d
print(ans)
 		 	 	   	  					 				  	   		