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
//package CodeForce;
 
import java.util.Scanner;
 
 
public class IncreasingSequence {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int d = input.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = input.nextInt();
        }
        int c = 0,m;
        for (int i = 1; i < n; i++) {
            if(a[i]<=a[i-1]){
               m = ((a[i-1]-a[i])/d) + 1;
                c += m;
              a[i] += m*d;
             
            }
          
        }
        System.out.println(c);
    }
}