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.Scanner;

public class Increasing_Sequence {
    public static void main(String args[]){
            Scanner in = new Scanner(System.in);
            int a, b;
            a= in.nextInt();
            b=in.nextInt();
            int c[]=new int[a];
            for(int i=0;i<a;i++)
                c[i] = in.nextInt();
                
            int max = 0 ;
            int temp = 0 , temp1=0 ;
            for(int i=0;i<a-1;i++)
                if(c[i]>=c[i+1]){
                    temp = c[i]-c[i+1];
                    temp1 = (temp/b)+1;
                    max+=temp1;
                    c[i+1]+=temp1*b;
                }
//          for(int i=0;i<a;i++)
//              System.out.print(c[i]+"  ");
//          System.out.println();
            System.out.println(max);
    }
}

