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 = raw_input().split()
n = [int(x) for x in n]
a_size = n[0]
d = n[1]

a = raw_input().split()
a = [int(x) for x in a]

count = 0

for i in range(a_size-1):
    if a[i] < a[i+1]:
        continue
    elif a[i] == a[i+1]:
        a[i+1] += d
        count += 1
    else:
        val = (a[i] - a[i+1])//d + 1
        count += val 
        a[i+1] += val*d
print count


        
