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.InputStreamReader;
import java.util.StringTokenizer;


public class C {
	public static void main(String[] args) throws Exception{
		int n = readInt();
		int m = readInt();
		double ans = 0;
		double exp[][] = new double[n+1][m+1];
		exp[0][0] = n;
		for(int i = 0; i< n; i++){
			for(int j = 0; j <= m; j++){
				exp[i+1][j] += exp[i][j]*1.0 - (double)exp[i][j]*((double)(m-j))/((double)(m*n-i));
				if(j < m){
					exp[i+1][j+1] += (double)exp[i][j]*((double)(m-j))/((double)(m*n-i));
				}
			}
		}
		for(int i = 1; i <= m; i++){
			double prob = i;
			prob/=n;
			prob*=exp[n][i];
			ans+= prob*(((double) i)/n);
		}
		System.out.println(ans);
	}
	static BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st = new StringTokenizer(" ");
	static String readString() throws Exception{
		while(!st.hasMoreTokens()){
			st = new StringTokenizer(stdin.readLine());
		}
		return st.nextToken();
	}
	static int readInt() throws Exception {
		return Integer.parseInt(readString());
	}
	static long readLong() throws Exception {
		return Long.parseLong(readString());
	}
}