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.*;
	
	public class IncreasingSequence{
	
		public static void main(String args[]){
		
			Scanner kbd = new Scanner(System.in);
			
			int N = kbd.nextInt();
			int D = kbd.nextInt();
			
			int a[] = new int[N];
			
			for(int i=0;i<N;i++)
				a[i] = kbd.nextInt();
			
			int count = 0;
			
			for(int i=0;i<N-1;i++){
				if(a[i]>=a[i+1]){
					
					int x = a[i]-a[i+1]+1;
					
					int temp_count = x/D;
					
					if(x%D!=0)
						temp_count++;
						
					a[i+1] += temp_count*D;
					
					count += temp_count;
					
				}
			}
			
			System.out.println(count);
			
		}
	}