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
#code by aanchaltiwari
import math
n, d = map(int, input().split())
l = list(map(int, input().split()))
i = 1
c = 0
while i < n:
    if l[i] <= l[i - 1]:
        diff = l[i - 1] - l[i]
        add = diff//d+1
        l[i] += add * d
        c = c + add
    i = i + 1
# print(l)
print(c)
