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
n, d = map(int, input().split())
arr = list(map(int, input().split()))

idx = 1
cnt = 0

while idx < n:

    if arr[idx] == arr[idx - 1]:
        arr[idx] += d
        cnt += 1
    elif arr[idx] < arr[idx - 1]:
        add = 1 + (arr[idx - 1] - arr[idx]) // d
        arr[idx] += d * add
        cnt += add
    idx += 1

print(cnt)
