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.*;
/**
 * Created by Zafar Mahmudov on 03.08.2014.
 */
public class A11 {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int d = scan.nextInt();
        int [] f = new int [2001];
        int i, ans = 0;
        for(i = 0; i < n; ++i) {
            f[i] = scan.nextInt();
        }
        for(i = 1; i < n; ++i) {
            if(f[i] <= f[i-1]) {
                ans += (((f[i-1] - f[i]) / d) + 1);
                f[i] += (((f[i-1] - f[i]) / d) + 1) * d;
            }
        }
        System.out.println(ans);
    scan.close();
    }
}
