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
def inc_seq(arr,d):
    count = 0
    for i in range(1,len(arr)):
        if arr[i]<=arr[i-1]:
            k = arr[i-1]-arr[i]
            div = (k//d)+1
            arr[i]+=d*div
            count+=div
    return count
    
nd = input().split()
n = int(nd[0])
d = int(nd[1])
arr = list(map(int,input().split()))
print(inc_seq(arr,d))