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
"""
codeforces increasing sequence 11A 
"""


a, b = [int(x) for x in input().split()]
seq = [int(x) for x in input().split()]

mini = 0

if len(seq)>1:
    for i in range(len(seq) - 1):
        if seq[i + 1] <= seq[i]:
            v = (seq[i] - seq[i + 1]) // b + 1
            seq[i + 1] += v * b
            mini += v

print(mini)
