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.Arrays;
import java.util.Scanner;


public class IncreasingSequence {
    int n, d;
    int[] b;
    private int getResult() {
        int count = 0;
        for(int i=1; i<n; i++) {
            if(b[i-1] >= b[i]) {
                count += ((b[i-1] - b[i]) / d) + 1;
                b[i] += d * (((b[i-1] - b[i]) / d) + 1);
            }
        }
        return count;
    }
    private void process() {
        Scanner scanner = new Scanner(System.in);
        n = scanner.nextInt();
        d = scanner.nextInt();
        b = new int[n];
        for(int i=0; i<n; i++) {
            b[i] = scanner.nextInt();
        }
        System.out.println(getResult());
    }
    
    public static void main(String[] args) {
        new IncreasingSequence().process();
    }
}
