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.awt.Point;
import java.awt.geom.Point2D;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;

/**
 *
 * @author Mojtaba
 */
public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer tokenizer = new StringTokenizer(reader.readLine());
        StringBuilder sb = new StringBuilder();

        int n = Integer.parseInt(tokenizer.nextToken());
        int d = Integer.parseInt(tokenizer.nextToken());
        int[] a = new int[n];
        int moves = 0;
        tokenizer = new StringTokenizer(reader.readLine());
        for (int i = 0; i < a.length; i++) {
            a[i] = Integer.parseInt(tokenizer.nextToken());
        }
        for (int i = 1; i < a.length; i++) {
            if (a[i] <= a[i - 1]) {
                int dif = a[i - 1] - a[i];
                int t = (dif / d) + 1;
                moves += t;
                a[i] += (t * d);
            }
        }
        sb.append(moves);

        System.out.println(sb.toString().trim());
    }
}