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.util.Scanner;

/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author ASUS
 */
public class NewClass {
    
    
    
public static void main(String[] args) {

    Scanner sc=new Scanner(System.in);
          double m,n;
                  
          n=sc.nextDouble();
          m=sc.nextDouble();
          
    if ( n == 1 ) {
        System.out. printf ("%.10f", 1. );
        
    }
    else
    if ( m == 1 ) {
         System.out. printf ("%.10f", 1. / n );
       
    }
    else
     System.out. printf ("%.10f", 1. / n + ( ( ( n - 1 ) /  n  ) * (  (m - 1 ) / ( n * m - 1 ) ) ) );
     //System.out. printf("%.10lf",1./n+(  ( ( n - 1 ) /  ( n ) )  ));

    System.out.println();
}
    
}