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.Arrays;
import java.util.Scanner;

public class CF011A {
    public static void main(String[] args) {
        Scanner s= new Scanner(System.in);
        int n = s.nextInt();
        int d = s.nextInt();
        int[] arr = new int[n];
        for(int i =0;i<n;i++){
            arr[i] = s.nextInt();
        }
        long count = 0;
        for(int i = 1;i<n;i++){
//            while(arr[i] <= arr[i-1]){
//                arr[i] += d;
//                count++;
//            }
            if(arr[i] <= arr[i-1]){
                if(arr[i] == arr[i-1]) {
                    arr[i] += d;
                    count++;
                }else{
                    int diff = arr[i-1] + 1 - arr[i];
                    if(diff % d == 0){
                        count += diff/d;
                        arr[i] = arr[i-1] + 1;
                    }else{
                        count = count + ((int)(diff/d) + 1);
                        arr[i] += ((int)(diff/d) + 1)*d;
                    }
                }
            }
//            System.out.println(Arrays.toString(arr));
        }
        System.out.println(count);
    }
}
