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.util.HashMap;
import java.util.Map;
import java.util.Scanner;


public class CProb {

    public static class BigDouble {
        int x;
        double d;
        public BigDouble(double d) {
            this.d = d;
            this.x = 0;
        }
        public void calibrate() {
            while (d >= 10) {
                d *= 0.1;
                x++;
            }
            while (d <= 0.1) {
                d *= 10;
                x--;
            }
        }
        public BigDouble multiply(BigDouble b) {
            BigDouble res = new BigDouble(0);
            res.d = this.d * b.d;
            res.x = this.x + b.x;
            res.calibrate();
            return res;
        }
        public BigDouble divide(BigDouble b) {
            BigDouble res = new BigDouble(0);
            res.d = this.d / b.d;
            res.x = this.x - b.x;
            res.calibrate();
            return res;
        }
        public BigDouble add(BigDouble b) {
            BigDouble res = new BigDouble(0);
            if (b.x > x) {
                res.x = b.x;
                res.d = b.d + d*Math.pow(10, x-b.x);
            } else {
                res.x = x;
                res.d = d + b.d*Math.pow(10, b.x-x);
            }
            res.calibrate();
            return res;
        }
        @Override
        public String toString() {
            Double res = d*Math.pow(10, x);
            return res.toString();
        }
    }
    
    static Map<Integer, BigDouble> mp = new HashMap<Integer, BigDouble>();

    public static BigDouble C(int n,int m) {
        BigDouble res = new BigDouble(1);
        if (mp.containsKey(n*1111+m)) {
            return mp.get(n*1111+m);
        }
        if (m>0 && mp.containsKey(n*1111+m-1)) {
            res = mp.get(n*1111+m-1).multiply(new BigDouble(1.0*(n-m+1)/m));
            mp.put(n*1111+m, res);
            return res;
        }
        if (n>m && mp.containsKey(n*1111+m+1)) {
            res = mp.get(n*1111+m+1).multiply(new BigDouble(1.0*(m+1)/(n-m)));
            mp.put(n*1111+m, res);
            return res;
        }
        for (int i = 1; i<=n; i++) {
            res = res.multiply(new BigDouble(i));
        }
        for (int i = 1; i<=m; i++) {
            res = res.multiply(new BigDouble(1.0/i));
        }
        for (int i = 1; i<=n-m; i++) {
            res = res.multiply(new BigDouble(1.0/i));
        }
        mp.put(n*1111+m, res);
        return res;
    }
    
    public static void main(String [] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        BigDouble res = new BigDouble(0);
        for (int k = 1; k <=n && k <=m; k++) {
            res = res.add(C(m-1,k-1).multiply(C(n*m-m,n-k)).multiply(new BigDouble(1.0*k/n)));
        }
        res = res.divide(C(n*m-1,n-1));
        System.out.println(res);
    }
}