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;
import java.io.PrintStream;
import java.util.Iterator;
import java.util.StringTokenizer;

/**
 * @author artyom
 */
public class IncreasingSequence implements Runnable {
    private BufferedReader in;
    private PrintStream out;
    private StringTokenizer tok;

    private void solve() throws IOException {
        int n = nextInt(), d = nextInt();
		int steps = 0, prev = nextInt();
		for (int i = 1; i < n; i++) {
			int cur = nextInt();
			if (cur <= prev) {
				int diff = 1 + (prev - cur) / d;
				steps += diff;
				prev = cur + d * diff;
			} else {
				prev = cur;
			}
		}
		out.println(steps);
	}

    //--------------------------------------------------------------
    public static void main(String[] args) {
        new IncreasingSequence().run();
    }

    @Override
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = System.out;
            tok = null;
            solve();
            in.close();
        } catch (IOException e) {
            System.exit(0);
        }
    }

    private int[] readArray(int n) throws IOException {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = nextInt();
        }
        return arr;
    }

    private static String join(Iterable<?> entries, CharSequence separator) {
        StringBuilder sb = new StringBuilder();
        for (Iterator<?> iterator = entries.iterator(); iterator.hasNext();) {
            sb.append(iterator.next());
            if (iterator.hasNext()) {
                sb.append(separator);
            }
        }
        return sb.toString();
    }

	private static String join(int[] entries, CharSequence separator) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0, n = entries.length - 1; i <= n; i ++) {
			sb.append(entries[i]);
			if (i < n) {
				sb.append(separator);
			}
		}
		return sb.toString();
	}

    private String nextToken() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    private short nextShort() throws IOException {
        return Short.parseShort(nextToken());
    }

    private int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    private long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
}