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.*;
public class MyClass {
    public static void main(String args[]) {
        Scanner sc=new Scanner(System.in);
		int n=sc.nextInt(),d=sc.nextInt();
		int[] arr=new int[n];
		for(int i=0;i<n;i++)
		    arr[i]=sc.nextInt();
		
		int moves=0;
		for(int i=0;i<n-1;i++){
		    if(arr[i]>=arr[i+1]){
		        int m=(1+(arr[i]-arr[i+1])/d);
		        moves+=m;
		        arr[i+1]+=d*m;
		    }
		    //System.out.println(moves);
		}
		System.out.println(moves);
    }
}
