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
n = input().split()
d = int(n[1])
n = int(n[0])
res = 0
a = list(map(int,input().split()))
for i in range(1,n):
    if a[i] <= a[i-1]:
       res = res + (a[i-1]-a[i]) // d +1
       a[i] += ((a[i-1]-a[i]) // d +1) * d
print(res)