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
import math
array_len, add = map(int, input().split())
numbers = list(map(int, input().split()))
counter = 0
moves = 0
current = 0
while counter < array_len - 1:
    current = math.ceil((numbers[counter] - numbers[counter + 1]) / add)
    if numbers[counter] - numbers[counter + 1] == 0:
        moves += 1
        numbers[counter + 1] += add
    elif numbers[counter] - numbers[counter + 1] > 0:
        moves += current
        if numbers[counter + 1] + (current * add) == numbers[counter]:
            moves += 1
            numbers[counter + 1] = numbers[counter + 1] + ((current + 1) * add)
        else:
            numbers[counter + 1] = numbers[counter + 1] + (current * add)
    counter += 1
print(moves)
