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 P11A {
    
    public static void main(String args[]){
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int d = scanner.nextInt();
        int ans = 0;
        int x=0, y;
        for (int i=0; i<n; i++){
            y = scanner.nextInt();
            if (x>=y){
                int k = (x-y)/d;
                y += k*d;
                while (y<=x){
                    y+=d;
                    k++;
                }
                ans += k;
            }
            x = y;
        }
        System.out.println(ans);
    }
}
