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.*;
public class C
{
	public static double[][] memo;
	public static int n;
	public static int m;
	
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		
		int n = in.nextInt();
		int m = in.nextInt();
		
		int same = m - 1;
		int other = n * m - m;
		
		double[][] dp = new double[n][same + 1];
		dp[0][0] = 1;
		for(int x = 1; x < dp.length; x++)
		{
			for(int y = 0; y < dp[0].length; y++)
			{
				dp[x][y] += dp[x - 1][y] * ((double)(other - (x - 1 - y)) / (same + other - (x - 1)));
				
				if(y > 0)
				{
					dp[x][y] += dp[x - 1][y - 1] * ((double)(same - (y - 1)) / (same + other - (x - 1)));
				}
			}
		}
		
		double result = 0;
		for(int z = 1; z <= Math.min(n, m); z++)
		{
			result += dp[n - 1][z - 1] * ((double)z / n);
		}
		
//		double result = 0;
//		for(int x = 1; x <= Math.min(n, m); x++)
//		{
////			double prob = 1;
////			for(int y = 1; y < x; y++)
////			{
////				prob *= (double)(m - y) / (n * m - y);
////			}
////			
////			for(int z = 0; z < n - x; z++)
////			{
////				prob *= (double)(n * m - m - z) / (n * m - x - z);
////			}
//			
//			memo = new double[n - 1][x];
//			for(int y = 0; y < memo.length; y++)
//			{
//				Arrays.fill(memo[y], -1);
//			}
//			
//			result += getProb(0, 0) * ((double)(x) / n);
//		}
		
		System.out.println(result);
	}
	
//	public static double getProb(int index, int left, int others)
//	{
//		if(index == memo.length)
//		{
//			if(left == 0)
//			{
//				return 1;
//			}
//			else
//			{
//				return 0;
//			}
//		}
//		else if(memo[index][left] != -1)
//		{
//			return memo[index][left];
//		}
//		else
//		{
//			double ret = ((double)others / (others + left)) * getProb(index + 1, left, others - 1);
//			
//			if(left > 0)
//			{
//				ret += ((double)left / (others + left)) * getProb(index + 1, left - 1, others);
//			}
//		}
//	}
	
//	public static double getProb(int index, int used)
//	{
//		if(index == memo.length)
//		{
//			if(used == memo[0].length - 1)
//			{
//				return 1;
//			}
//			else
//			{
//				return 0;
//			}
//		}
//		else if(memo[index][used] != -1)
//		{
//			return memo[index][used];
//		}
//		else
//		{
//			double ret = (double)(n * m - m - (index - used)) / (n * m - 1 - index) * getProb(index + 1, used);
//			
//			if(used < m - 1)
//			{
//				ret += (double)(m - 1 - used) / (n * m - 1 - index) * getProb(index + 1, used + 1);
//			}
//			
//			return ret = memo[index][used];
//		}
//	}
}