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
a,b=map(int,raw_input().split())
arr=map(int,raw_input().split())
c=0
for i in range(1,a):
    # print c
    if arr[i]>arr[i-1]:
        continue
    else:
        if arr[i]<=arr[i-1]:
            if (arr[i-1]-arr[i]+1)%b==0:
                c=c+((arr[i-1]-arr[i]+1)/b)
                arr[i]=arr[i]+((arr[i-1]-arr[i]+1))
                
            else:
                c=c+((arr[i-1]-arr[i]+1)/b +1)
                arr[i]=arr[i]+(b*((arr[i-1]-arr[i]+1)/b +1))
                
        # while(arr[i]<=arr[i-1]):
        #   c=c+1
        #   arr[i]=arr[i]+b
print c
