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.*;
import java.util.Locale;
import java.util.Scanner;

/**
 * Author: Sergey Paramonov
 * Date: 27.07.14
 * Time: 19:47
 */
public class MemSQL_20140727_C {

    Scanner scanner = new Scanner(System.in);
    BufferedReader buffered = new BufferedReader(new InputStreamReader(System.in));
    StreamTokenizer input = new StreamTokenizer(buffered);

    static PrintWriter output = new PrintWriter(new BufferedOutputStream(System.out));

    int nextInt() throws Exception {
        input.nextToken();
        return (int) input.nval;
    }

    static void flushAndClose() {
        output.flush();
        System.out.flush();
        output.close();
    }

    void main() throws Exception {
        double n = nextInt();
        double m = nextInt();
        double ans = 1.0/n;
        if (m > 1) {
            ans += (1.0 - 1.0/n) * (m-1.0)/(n*m - 1.0);
        }
        System.out.printf(Locale.ENGLISH, "%.10f", ans);
    }

    public static void main(String[] args) throws Exception {
        new MemSQL_20140727_C().main();
        flushAndClose();
    }

}