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

def main():
    n,d = map(int,input().split())
    arr = list(map(int,input().split()))
    moves = 0
    for i in range(n-1,0,-1):
        if arr[i] <= arr[i-1]:
            count = int(math.ceil((arr[i-1]+1-arr[i])/d))
            arr[i] += count*d
            moves += count
            for j in range(i,n-1):
                if arr[j] >= arr[j+1]:
                    count = int(math.ceil((arr[j]+1-arr[j+1])/d))
                    arr[j+1] += count*d
                    moves += count

    print(moves)


main()
