Problem: Alex enjoys performing magic tricks. He has a trick that requires a deck of n cards. He has m identical decks of n different cards each, which have been mixed together. When Alex wishes to perform the trick, he grabs n cards at random and performs the trick with those. The resulting deck looks like a normal deck, but may have duplicates of some cards.

The trick itself is performed as follows: first Alex allows you to choose a random card from the deck. You memorize the card and put it back in the deck. Then Alex shuffles the deck, and pulls out a card. If the card matches the one you memorized, the trick is successful.

You don't think Alex is a very good magician, and that he just pulls a card randomly from the deck. Determine the probability of the trick being successful if this is the case.

Input

First line of the input consists of two integers n and m (1 ≤ n, m ≤ 1000), separated by space — number of cards in each deck, and number of decks.

Output

On the only line of the output print one floating point number – probability of Alex successfully performing the trick. Relative or absolute error of your answer should not be higher than 10 - 6.

Examples

Input

2 2


Output

0.6666666666666666


Input

4 4


Output

0.4000000000000000


Input

1 2


Output

1.0000000000000000

Note

In the first sample, with probability <image> Alex will perform the trick with two cards with the same value from two different decks. In this case the trick is guaranteed to succeed.

With the remaining <image> probability he took two different cards, and the probability of pulling off the trick is <image>.

The resulting probability is <image>

Solution (in JAVA):

Solution:
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskC {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        double[] f = new double[1000001];
        f[0] = 0;
        for (int i = 1; i < f.length; ++i) {
            f[i] = f[i - 1] + Math.log(i);
        }
        int n = in.nextInt();
        int m = in.nextInt();
        double res = 0;
        for (int i = 0; i <= m - 1 && i <= n - 1; ++i) {
            double p = 0;
            double C1 = f[m - 1] - f[i] - f[m - i - 1];
            double C2 = f[m*n - m] - f[n - 1 - i] - f[m*n-m-n+1+i];
            double C3 = f[m*n - 1] - f[n - 1] - f[m*n - n];
            res += Math.exp(C1 + C2 - C3) * (i + 1) / n;
        }
        out.printf("%.20f\n", res);
    }
}

class InputReader {
    BufferedReader bufReader;
    StringTokenizer stringTokenizer;

    public InputReader(InputStream stream) {
        bufReader = new BufferedReader(new InputStreamReader(stream));
    }

    public String next() {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            try {
                String line = bufReader.readLine();
                if (line == null) {
                    return null;
                }
                stringTokenizer = new StringTokenizer(line);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        return stringTokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    }