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
from math import ceil
a=input().split()
b=input().split()
c=0
for i in range (1,int(a[0])):
    if int(b[i])<=int(b[i-1]):
        d=ceil((int(b[i-1])-int(b[i])+1)/int(a[1]))
        c+=d
        b[i]=int(b[i])+int(a[1])*d
print(c)
