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

splits = input().split()
n,d = int(splits[0]), int(splits[1])

result = 0
numbers = input().strip().split()
numbers = [int(idx) for idx in numbers]
for i in range(1,n):
    diff = numbers[i] - numbers[i-1]
    if diff <= 0:
        diff *= -1
        times = math.floor(diff/d) + 1
        numbers[i] += times * d
        result += times
# print(numbers)
print(result)
