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,d=map(int,input().split())
l1 = list(map(int, input().split()))

l = l1.copy()
l.reverse()

c =0

for i in range(1,len(l1)):
    if l1[i] <= l1[i-1]:
        nr_ofSteps = (l1[i-1] - l1[i]) // d+1
        l1[i] += nr_ofSteps * d
        c += nr_ofSteps
print(c)
