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.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

public class C
{
	private static BigDecimal[] fac;

	public static void main(String[] args) throws IOException
	{
		Scanner in = new Scanner(System.in);

		int n = in.nextInt();
		int m = in.nextInt();

		double [][] dp = new double[n+1][m+1];
		boolean [][] reach = new boolean[n+1][m+1];

		dp[0][0] = 1;
		reach[0][0] = true;
		for(int till = 0 ; till < n ; till++)
			for(int c = 0 ; c <= m ; c++)
				if(reach[till][c])
				{
					dp[till+1][c] += (n*m - m - (till-c))*dp[till][c]/(n*m-till);
					reach[till+1][c] = true;
					if(c+1 <= m)
					{
						dp[till+1][c+1] += ((m-c)*dp[till][c])/(n*m-till);
						reach[till+1][c+1] = true;
					}
				}

		double res = 0;
		for(int c = 1 ; c <= m ; c++)
			if(reach[n][c])
			{
				res += dp[n][c]*(c/(double)n)*(c/(double)n);
			}

		System.out.println(res*n);
	}
}