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 = tuple(int(i) for i in raw_input().split(" "))
nums = tuple(int(i) for i in raw_input().split(" "))

answer = 0
c = nums[0] + 1
for k in nums[1:]:
  m = max(0, int(ceil(float(c - k) / d)))
  c = k + m * d + 1
  answer += m

print answer
