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
#!/usr/bin/env python2.7

d = int(raw_input().split(' ')[1])
seq = map(int, raw_input().split(' '))
count = 0

def func(a, b):
    global count
    tmp = (a - b) / d + 1 if a >= b else 0
    count += tmp
    return b + d * tmp

reduce(func, seq)
print count

				 	   	 	   	 	 	   			