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, input().strip().split())
lst = list(map(int, input().strip().split()))
count = 0
for i in range(1, n):
    if (lst[i] > lst[i - 1]):
        continue
    else:
        count += ceil(max(lst[i - 1] -lst[i],1)/d)
        lst[i] += ceil(max(lst[i - 1] -lst[i],1)/d)* d
        if lst[i]<=lst[i-1]:
            lst[i]+=d
            count+=1
        # while (lst[i - 1] >= lst[i]):
print(count)
