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 CF452C {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		int m = Integer.parseInt(st.nextToken());
		if (n == 1) {
			System.out.println(1);
			return;
		}
		// probability of one card chosen from m decks into a mixed deck
		//	a = choose(n * m - 1, n - 1) / choose(n * m, n)
		//		= n / (n * m) = 1 / m
		// probability of one card chosen twice from a mixed deck of n cards
		//	b = 1 / n / n
		// combinations of one card from m decks
		//	c = m * n
		// linearity of expectation
		//	a * b * c = 1 / n
		double p1 = 1.0 / n;
		// probability of two cards chosen from m decks into a mixed deck
		//	a = choose(n * m - 2, n - 2) / choose(n * m, n)
		//		= n * (n - 1) / (n * m) / (n * m - 1) = (n - 1) / m / (n * m - 1)
		// probability of two cards chosen from a mixed deck of n cards
		//	b = 2 / n / n
		// combinations of two matching cards from m decks
		//	c = choose(m, 2) * n = m * (m - 1) * n / 2
		// linearity of expectation
		//	a * b * c = (m - 1) * (n - 1) / n / (n * m - 1);
		double p2 = (double) (m - 1) * (n - 1) / n / (n * m - 1);
		System.out.println(p1 + p2);
	}
}