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.Scanner;

public class problem107 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k  =sc.nextInt();
		int ar[] = new int[n];
		for(int i=0;i<n;i++)
		{
			ar[i] = sc.nextInt();
			
		}
		
		int count = 0;
		for(int i=0;i<n-1;i++)
		{int ans=0;
			if(ar[i]>=ar[i+1])
			{
				int diff = ar[i] - ar[i+1];
				ans = (diff/k)+1;
				ar[i+1] = ar[i+1]+ans*k;
			}
			count = count +ans;
		}
      System.out.println(count);
	}

}
