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.*;

//Mann Shah [ DAIICT ].

public class Main {
	public static void main(String[] Args) {
		Scanner in = new Scanner(System.in);
		int mod = 1000000007;
		
		int n = in.nextInt();
		int d = in.nextInt();
		int[] a = new int[n];
		int c=0;
		for(int i=0;i<n;i++) {
			a[i]=in.nextInt();
		}
		for( int i = 1 ; i < n ; i++ ) {
			if(a[i]<=a[i-1]) {
				int x= a[i-1]-a[i];
				if(x==0) {
					c++;
					a[i]=a[i]+d;
				}
				else {
					int xx =(int) Math.ceil((double)(x+1)/(double)d);
					//System.out.println(xx);
					c+=xx;
					a[i]=a[i]+xx*d;
				}
			}
		}
		System.out.println(c);
		
		in.close();
	}
}
