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.IOException;
import java.io.InputStreamReader;

public class A {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String[] S = in.readLine().split(" ");
        int n = Integer.parseInt(S[0]);
        int d = Integer.parseInt(S[1]);
        int[] A = new int[n];
        S = in.readLine().split(" ");
        for (int i = 0; i < n; i++)
            A[i] = Integer.parseInt(S[i]);
        int ans = 0;
        for (int i = 1; i < n; i++)
            if (A[i] <= A[i - 1]) {
                int temp = (int) Math.ceil((A[i - 1] - A[i] + 1) * 1.0 / d);
                A[i] += temp * d;
                ans += temp;
            }
        System.out.println(ans);
    }
}
