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
n,d = map(int, input().split())
arr = list(map(int, input().split()))

ops = 0
for i in range(1,n):
    if arr[i] <= arr[i-1]:
        increase = arr[i-1] - arr[i]
        p = (increase//d)+1
        arr[i] += d*p
        ops += p
print(ops)
	  		  	 	  	 	 	 	 	   			 		