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
a,b = map(int,input().split())

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

i = 0
count = 0
d.append(19232931932)
while( i < a ):
    if d[i] < d[i + 1]:
        i += 1
    else:
        num = ((d[i ] - d[i + 1] ) / b ) + 1
        num = int(num)
        count += num
        d[i + 1] += num * b
        i += 1




print(count)


