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())
l=  list(map(int, input().split()))
x=0
i=0
for i in range(n-1):
    if(l[i]>=l[i+1]):
        dif= l[i]- l[i+1]
        s= int(dif/d)+1
        l[i+1]= l[i+1]+s*d
        x= x+s
print(x)
