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 static java.lang.Math.abs;
import static java.lang.Math.ceil;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner cin = new Scanner(System.in);
        int n = cin.nextInt();
        int d = cin.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = cin.nextInt();
        }
        int c = 0;
        for (int i = 1; i < n; i++) {
            int j = (int) ceil((double) (a[i - 1] - a[i] + 1) / d);
            if (j < 0)
                continue;
            c += j;
            a[i] += d * j;
        }
        System.out.println(c);
    }
}
