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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Locale;

public class CF452C {
    private static BufferedReader input = new BufferedReader(new InputStreamReader(System.in));

    static String readln() throws IOException {
        String line = input.readLine();
        return line;
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        String input = CF452C.readln();

        String[] array = input.split(" ");
        int m = Integer.parseInt(array[0]);
        int n = Integer.parseInt(array[1]);

        solution(m, n);
    }

    public static void solution(int m, int n) {
        double res = 0.0;
        double p = 1.0;
        for (int i = 1; i < m; i++) {
            p *= 1.0 * (m * n - n - i + 1) / (m * n - 1 - i + 1);
        }
        int i = 0;
        while (i < Math.min(m, n)) {
            res += p * (i + 1) / m;
            i++;
            p *= 1.0 * (n - 1 - i + 1) / i * (m - i) / (m * n - m - n + i + 1);
        }
        System.out.println(res);
    }
}