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.io.PrintWriter;
import java.util.*;


public class C {	
	BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter out;
    
	public void solve() throws IOException {				
		int N = nextInt();
        int M = nextInt();


        double pick = N;
        double ans = 0;
        for (int c = 1; c <= N; c++) {
            double P = 1;
            for (int i = 0; i < c; i++) {
                P *= (double)(M - i) / (double)(N * M - i);
            }
            for (int i = 0; i < N-c; i++) {
                P *= (double)(M*(N-1) - i) / (double)(N * M - c - i);
            }
//            out.println(c + ": " + P);
            P *= pick;
            pick = pick * (N-c) / (c+1);
//            P *= nCr(N, c);
            P *= ((double)(c * c) / (double)(N * N));
            ans += P;
        }
        ans *= N;
        out.println(ans);
	}

    public long nCr(int n, int k){
        long ans = 1;
        int cb[] = new int[k];

        for (int i=0; i<k; i++)
            cb[i] = i + 1;
        for (int i=n; i>=n-k+1; i--){
            ans *= i;
            for (int j=0; j<cb.length; j++)
                if (ans % cb[j] == 0){
                    ans /= cb[j];
                    cb[j] = 1;
                }
        }
        return ans;
    }
	
	/**
	 * @param args
	 */
	public static void main(String[] args) {
		new C().run();
	}
	
	public void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
            out = new PrintWriter(System.out);
            solve();
            reader.close();
            out.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

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

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

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

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

}