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 IncreasingSequence {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int d = sc.nextInt();
        int[] seq = new int[n];
        for(int i=0; i< n; i++){
            seq[i] = sc.nextInt();
        }
        
        int ans = 0;
        if(n == 1){
            ans = 1;
        }
        else if(n > 1){
            for(int i=1; i<n; i++){
                if(seq[i] <= seq[i-1]){
                    int c = ((seq[i-1] - seq[i])/d) + 1;
                    seq[i] += c*d;
                    ans +=c;
                }
            }
        }
        System.out.println(ans);
    }
}