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


temp = list(map(int, input().split()))

n = temp[0]
d = temp[1]


b = list(map(int, input().split()))



steps = 0

for i in range(1,len(b)):

    

    dif = b[i-1] - b[i]


    if (dif >= 0): 
        steps_i = dif // d + 1
        steps += steps_i
        b[i] += steps_i * d 

   # print(b)
   # print(steps)


print(steps)




