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
__author__ = 'Will'


n, d = map(int, raw_input().split())

arr = map(int, raw_input().split())

moves = 0
for i in range(1,n):
    if arr[i-1] < arr[i]:
        continue
    else:
        diff = abs(arr[i]-arr[i-1])
        temp = max(0, diff/d+1)
        arr[i] += temp * d
        moves+= temp

        # if diff == 0:
        #     moves+=1
        #     arr[i]+= d
        # else:
        #     moves+= diff/d
        #     temp = diff%d
        #     if temp !=0:
        #         moves+= 1
        #     arr[i] += d * (diff/d)
        #     if temp != 0:
        #         arr[i]+=d
print moves