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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author janux
 */
public class A {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(st.nextToken());
        int d = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(in.readLine());
        int[] arr = new int[n];
        for (int i = 0; i < n; ++ i) {
            arr[i] = Integer.parseInt(st.nextToken());
        }
        int sol = 0;

        for (int i = 1; i < n; ++ i) {
            if (arr[i - 1] < arr[i]) continue;
            int df = arr[i - 1] - arr[i];
            if (df == 0) {
                arr[i] += d;
                ++ sol;
            }
            else {
                int q = (df/d) + 1;
                sol += q;
                arr[i] += d * q;
            }
        }        
        System.out.println(sol);
    }
}
