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.InputStream;
import java.io.PrintStream;
import java.util.Scanner;

public class CFS452C {

	public final static String IN_FILE = "test/CFS452C.in";
	public final static String OUT_FILE = "test/CFS452C.out";

	private static Scanner IN;

	public static void main(String[] args) throws Exception {
		// InputStream in = new FileInputStream(IN_FILE);
		//
		// @SuppressWarnings("resource")
		// PrintStream out = new PrintStream(OUT_FILE);

		InputStream in = System.in;
		PrintStream out = System.out;

		IN = new Scanner(in);

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

		double p = 0.0;

		if (n == 1 && m == 1) {
			p = 1.0;
		} else {
			p = 1.0 / n + 1.0 * (n - 1) / n * (m - 1) / (n * m - 1);
		}

		out.println(String.format("%.16f", p));
	}
}