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 MainB {
    public static void main(String[]args){
        
        Scanner sc = new Scanner(System.in);
        
        int n = sc.nextInt();
        int d = sc.nextInt();
        int ans = 0;
        int A[] = new int[n];
        for (int i = 0; i<n; i++){
            A[i] = sc.nextInt();    
        }   
        for (int i = 0; i<n-1;i++){
            int k = count(A[i], A[i+1], d);
            if (k!=0){
                A[i+1] = A[i+1] + count(A[i], A[i+1], d) * d;   
                ans = ans + k;
            }
            
        }
        
        System.out.println(ans);
    }
    
    public static int count(int a0, int an, int d){
        if (a0-an>=0){          
            if (a0-an % d == 0 && a0-an != 0){return (a0-an)/d + 1;}
            else {return (a0-an)/d+1;}
        }
        else return 0;
    }
}


