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
//package com.company;

import java.util.Scanner;

public class IncreasingSequence {

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