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.lang.*;
import java.io.*;
import java.util.*;
import java.math.*;

public class Main {
    public static void main(String[] args) {
        new Solver().run();
    }
}

class Solver {

    void run() {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        //in = new BufferedReader(new FileReader("tree.in"));
        //out = new PrintWriter(new File("tree.out"));
        solve();
        out.close();
    }

    void solve() {
        int n = nextInt();
        int m = nextInt();
        if (n == 1 && m == 1) out.printf("%.9f", 1.0);
        else out.printf("%.9f", 1.0 / n * (1.0 + (m - 1.0) * (n - 1.0) / (n * m - 1.0)));
    }

    StringTokenizer tok;
    BufferedReader in;
    PrintWriter out;

    String next() {
        if (tok == null || !tok.hasMoreElements()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tok.nextToken();
    }

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

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    BigInteger nextBigInteger() {
        return new BigInteger(next());
    }
}