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
l1 = [int(x) for x in input().split()]
n,d = l1[0],l1[1]
l2 = [int(x) for x in input().split()]
ans0=sum(l2)
i=1
while i<len(l2):
    difference = l2[i-1]-l2[i]
    if difference>0:
        l2[i]+=int((l2[i-1]-l2[i])/d)*d
        #print(int((l2[i-1]-l2[i])/d),l2[i])
        l2[i]+=d
    elif difference==0:
        l2[i]+=d
    i+=1    
#print(l2)
    

print((sum(l2)-ans0)//d)