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
from __future__ import division
import math
def increasing_sequence (length,increment,sequence):
    count = 0
    for index in range (length):
        if index + 1 != length:
            diff = sequence[ index+1 ] - sequence[ index ]
            if diff < 0:
                sequence[index+1] += int (math.ceil(abs(diff)/increment)*increment)
                if sequence[index+1] == sequence[index]:
                    sequence[index+1] += increment
                    count += 1
                count += int(math.ceil(abs(diff)/increment)) 
            elif diff == 0:
                sequence[index+1] += increment
                count += 1
    print count


length,increment = map(int,raw_input().split())
sequence = list(map(int,raw_input().split()))
increasing_sequence(length,increment,sequence)
             