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.InputStreamReader;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.ArrayList;
import java.util.HashSet;

public class Main {
    private static StreamTokenizer in;
    private static PrintWriter out;
    private static BufferedReader inB;
    
    private static int nextInt() throws Exception{
        in.nextToken();
        return (int)in.nval;
    }
    
    private static String nextString() throws Exception{
        in.nextToken();
        return in.sval;
    }
    
    static{
        inB = new BufferedReader(new InputStreamReader(System.in));
        in = new StreamTokenizer(inB);
        out = new PrintWriter(System.out);
    }
    
    public static void main(String[] args)throws Exception{
        int n = nextInt(), d = nextInt();
        int[] b = new int[n];
        
        for(int i = 0; i<n; i++)b[i] = nextInt();
        
        int count = 0;
//      m:for(;;) {
//          boolean good = true;
//          for(int i = n - 1; i>=1; i--) {
//              while(b[i] <= b[i-1]) { b[i]+=d; good = false; count++;}
//          }
//          if(good)break;
//      }

        for(int i = 1; i<n; i++) {
            //while(b[i] <= b[i-1]) {b[i] += d; count++;}
            if(b[i] <= b[i-1]) {
                int col = (b[i-1] - b[i])/d + 1;
                count += col;
                b[i] += (d * col);
            }
        }
        
        System.out.println(count);
    }
}
