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.util.*;


public class Main {


	public static class pair implements Comparable<pair>
	{
		int a;
		int b;
		public pair(int pa, int pb)
		{
			a = pa; b= pb;
		}
		@Override
		public int compareTo(pair o) {
			if(this.a < o.a)
				return -1;
			if(this.a > o.a)
				return 1;
			return Integer.compare(o.b, this.b);
		}
	}
	

	//int n = Integer.parseInt(in.readLine());
	//String[] spl = in.readLine().split(" ");

	public static double[] logF;
	
	public static double logC(int N, int M)
	{
		return logF[N]-logF[M]-logF[N-M];
	}
	
	public static void main (String[] args) throws Exception
	{	
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] spl = in.readLine().split(" ");
		int n = Integer.parseInt(spl[0]);
		int m = Integer.parseInt(spl[1]);
		logF = new double[n*m+5];
		logF[0] = 0;
		for(int i=1; i<logF.length; i++)
		{
			logF[i] = logF[i-1] + Math.log(i);
		}
		//System.out.println(logF[5]);
		double num = 0;
		double c2 = logC(n*m,n);
		for (int k = 1; k <= n; k++) {
			if(k<=m && n-k<=(n-1)*m)
			{
				double c1 = logC(m,k) + logC((n-1)*m, n-k);
				num+= Math.exp(c1+2*Math.log(k)-c2-Math.log(n));
				if(Double.isInfinite(num))
					System.out.println(k);
			}
		}
		System.out.println(num);
	}
}