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
import java.util.*;
public class CAKEDOOM{
public static void main(String[] arcs){
Scanner sc = new Scanner(System.in);
int N = sc.nextInt();
int D = sc.nextInt();
int[] array = new int[N];
for(int a=0;a<N;a++)array[a]=sc.nextInt();
long ans = 0;
for(int a=1;a<N;a++){
if(array[a-1]>=array[a]){
int change = 1;
change = array[a-1]-array[a];
change/=D;
change++;
array[a]+=change*D;
ans+=change;
}
}
System.out.println(ans);
}
}