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
c = str(input()).split(' ')
c = [int(val) for val in c]
n = c[0]
d = c[-1]
p = str(input()).split(' ')
p = [int(val) for val in p]
count = 0
for i in range(n-1):
    if p[i] >= p[i+1]:
        count += (1 + (p[i] - p[i + 1])//d)
        p[i+1] += (1+(p[i]-p[i+1])//d)*d
print(count)
