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 = input().split()
n = int(n)
d = int(d)
a = input().split()
count = 0
a[0] = int(a[0])
for i in range(1, len(a)):
    a[i] = int(a[i])
    if a[i] <= a[i - 1]:
        count += (a[i - 1] - a[i])//d + 1
        a[i] += ((a[i - 1] - a[i])//d + 1)*d 
print(count)
			 		   	  	   	   		 	 	   	