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 Problem2 {

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