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

import math

class Solution:
    def __init__(self):
        return

    def seq(self, n, d, lis):
        ret, prev = 0, lis[0]
        for i in range(1, len(lis)):
            if lis[i] <= prev:
                v = max(1,math.ceil((prev - lis[i])/d))
                if v*d + lis[i] == prev:
                    v += 1
                prev = v*d + lis[i]
                ret += v
            else:
                prev = lis[i]
        return ret


s = Solution()
n,d =  map(int,input().split())
lis= list(map(int,input().split()))
print(s.seq(n,d,lis)) 


