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
from math import ceil
n,d = map(int, str(raw_input()).split())
a = map(int, str(raw_input()).split())
total = 0
previous = 0
for i in a:
    if i>previous:
        previous = i
        continue
    x = abs((i-previous)/float(d))
    if x == int(x):
        x += 1
    x = int(ceil(x))
    total += x
    i = i+x*d
    previous = i
print total
