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.*;
import java.io.*;
import java.math.*;
public class Main{
public static void main(String... args)throws IOException{
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
String[] temp = br.readLine().split(" ");
int n = Integer.parseInt(temp[0]);
int d = Integer.parseInt(temp[1]);
long[] t = new long[n];
temp = br.readLine().split(" ");
for (int i=0; i<n; i++){
  t[i] = Integer.parseInt(temp[i]);
}

long sum = 0;
for (int i=1; i<n; i++){
  long diff = t[i]-t[i-1];
  if (diff<0){
    long x = (((diff*(-1)))/d)+1;
    t[i]+=x*d;
    sum+=x;
  } else if (diff==0){
    long x = 1;
    t[i]+=x*d;
    sum+=x;
  }
}
System.out.println(sum);

}
}