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


def solve(arr, n, d):
    count = 0
    for i in range(1, n):
        if arr[i - 1] > arr[i]:
            v = ceil((arr[i - 1] - arr[i]) / d)
            count += v
            arr[i] += v * d
        if arr[i - 1] == arr[i]:
            count += 1
            arr[i] += d
    return count


def main():
    vars = list(map(int, input().split(" ")))
    arr = list(map(int, input().split(" ")))
    # for i in range(n):
    #     arr.append(list(map(int, list(input()))))
    print(solve(arr, *vars))


main()
