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.*;
import static java.lang.Math.*;

public class Main{
    public static void main(String[] args){
        new Main().run();
    }

    void run(){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int d = sc.nextInt();
        long[] b = new long[n];
        for(int i = 0; i < n; i++)b[i] = sc.nextLong();
        int ans = 0;
        for(int i = 1; i < n; i++){
            if(b[i-1] >= b[i]){
                int v = (int)(b[i-1]-b[i] + d) / d;
                ans += v;
                b[i] += 1l * d * v;
            }
        }
        System.out.println(ans);
    }
}
