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.InputStream;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.util.ArrayList;

public class C {

    static StringBuilder sb=new StringBuilder();
    static void parse(String l, int[] here) {
        sb.setLength(0);
        int len=l.length(), j=0;
        for (int i=0; i<len; i++) {
            char c=l.charAt(i);
            if(c==' ') {
                here[j++]=Integer.parseInt(sb.toString());
                sb.setLength(0);
            } else {
                sb.append(c);
            }
        }
        if(sb.length()>0) {
            here[j++]=Integer.parseInt(sb.toString());
        }
    }
    
    static void run_stream(InputStream ins) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String[] nm=br.readLine().split(" ");
        int n=Integer.parseInt(nm[0]);
        int m=Integer.parseInt(nm[1]);
        
        long t0=System.currentTimeMillis();
        
        BigInteger nmCn=nCk(n*m, n), p=BigInteger.ZERO;
        
        BigInteger mCi=new BigInteger(Integer.toString(m));
        BigInteger n_1mCn_i=nCk((n-1)*m, n-1);
        p=p.add(mCi.multiply(n_1mCn_i));
        
        for (int i=2; i<=Math.min(n, m); i++) {
            mCi=nCk(m, i);
            n_1mCn_i=n_1mCn_i.multiply(new BigInteger(Integer.toString(n-i+1))).divide(new BigInteger(Integer.toString((n-1)*m-(n-i))));

            p=p.add(mCi.multiply(n_1mCn_i).multiply(new BigInteger(Integer.toString(i*i))));
        }
        
        MathContext ctx=new MathContext(10);
        BigDecimal ret=new BigDecimal(p);
        ret=ret.divide(new BigDecimal(nmCn), ctx).divide(new BigDecimal(Integer.toString(n)), ctx);
        
        System.out.println(ret);
        
        //System.out.println(System.currentTimeMillis()-t0);
    }

    public static void main(String[] args) throws IOException {
        run_stream(System.in);
    }

    
    
    public static BigInteger nCk(int n, int k) {
        if(k>n) {
            return BigInteger.ZERO;
        }
        
        BigInteger ret=BigInteger.ONE;
        for (int i=Math.max(k+1, n-k+1); i<=n; i++) {
            ret=ret.multiply(new BigInteger(Integer.toString(i)));
        }
        
        if(k>=n-k) {
            ret=ret.divide(factorial(n-k));
        } else {
            ret=ret.divide(factorial(k));
        }
        
        return ret;
        
    }

    
    static ArrayList<BigInteger> fac_cache2; 
    static {
        fac_cache2=new ArrayList<>();
        fac_cache2.add(BigInteger.ONE);
    }
    
    static ArrayList<BigInteger> _factorial(int n) {
        ArrayList<BigInteger> l=fac_cache2;
        BigInteger bi=l.get(l.size()-1);
        for (int i=l.size(); i<=n; i++) {
            bi=bi.multiply(new BigInteger(Integer.toString(i)));
            l.add(bi);
        }
        return l;
    }
    
    public static BigInteger factorial(int n) {
        _factorial(n);
        return fac_cache2.get(n);
    }

}