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 main():
    list_size, add_int = [int(x) for x in raw_input().split()]
    results = [int(i) for i in raw_input().split()]
    number_of_increments = 0
    benchmark = 0
    
    for index in xrange(1, len(results)):
        if results[index] <= results[index-1]:
            benchmark = int(math.ceil((results[index-1]-results[index])/add_int))
            results[index] += (add_int * benchmark)
            number_of_increments += benchmark
        if results[index] == results[index-1]:
            results[index] += add_int
            number_of_increments += 1
    print number_of_increments 

if __name__ == '__main__':
    main()