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
import math
get_ints = lambda: map(int, raw_input().split())

n, d = get_ints()
seq = get_ints()

cur = seq[0]
total = 0
for i in seq[1:]:
    if cur >= i:
        n = int(math.ceil(float(cur - i + 1) / d))
        total += n
        cur = i + n * d
    else:
        cur = i

print total
