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
def incr(a,b,d):
    c=a-b
    x=c//d
    return x+1
n,d=[int(x) for x in input().split()]
l=[int(x) for x in input().split()]
c=0
for i in range(1,n):

    if l[i-1]>=l[i]:
        k=incr(l[i-1],l[i],d)
        c+=k
        l[i] = l[i]+k*d
print(c)