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

count,n=map(int,raw_input().split(' '))
num=0
a=map(int,raw_input().split(' '))
for i in range(1,len(a)):
    if a[i]<a[i-1]:
        A=1 if (a[i-1]-a[i])%n!=0 else 0
        num+=ceil(1.0*(a[i-1]-a[i])/n)
        a[i]+=((a[i-1]-a[i])/n+A)*n
    if a[i]==a[i-1]:
        num+=1
        a[i]+=n
print int(num)
