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 f(a):
    if a>0:
        return a
    else:
        return 0

temp = raw_input().split()
n, d = int(temp[0]), int(temp[1])

tab = raw_input().split()
for i in range(len(tab)):
    tab[i] = int(tab[i])

res = 0

for i in range(1,len(tab)):
    res += f((tab[i-1]-tab[i])/d+1)
    tab[i] += f(((tab[i-1]-tab[i])/d+1)*d)

#print tab

print res
