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
n , d = map(int , input().split())
arr = list(map(int,input().split()))
res = 0

for i in range(1 , n):
    if arr[i] <= arr[i- 1]:
        x = arr[i - 1] - arr[i]
        res += x // d + 1
        arr[i] = arr[i] + (x // d + 1 ) * d
    else:
        pass

print(res)


