Problem: The dragon and the princess are arguing about what to do on the New Year's Eve. The dragon suggests flying to the mountains to watch fairies dancing in the moonlight, while the princess thinks they should just go to bed early. They are desperate to come to an amicable agreement, so they decide to leave this up to chance.

They take turns drawing a mouse from a bag which initially contains w white and b black mice. The person who is the first to draw a white mouse wins. After each mouse drawn by the dragon the rest of mice in the bag panic, and one of them jumps out of the bag itself (the princess draws her mice carefully and doesn't scare other mice). Princess draws first. What is the probability of the princess winning?

If there are no more mice in the bag and nobody has drawn a white mouse, the dragon wins. Mice which jump out of the bag themselves are not considered to be drawn (do not define the winner). Once a mouse has left the bag, it never returns to it. Every mouse is drawn from the bag with the same probability as every other one, and every mouse jumps out of the bag with the same probability as every other one.

Input

The only line of input data contains two integers w and b (0 ≤ w, b ≤ 1000).

Output

Output the probability of the princess winning. The answer is considered to be correct if its absolute or relative error does not exceed 10 - 9.

Examples

Input

1 3


Output

0.500000000


Input

5 5


Output

0.658730159

Note

Let's go through the first sample. The probability of the princess drawing a white mouse on her first turn and winning right away is 1/4. The probability of the dragon drawing a black mouse and not winning on his first turn is 3/4 * 2/3 = 1/2. After this there are two mice left in the bag — one black and one white; one of them jumps out, and the other is drawn by the princess on her second turn. If the princess' mouse is white, she wins (probability is 1/2 * 1/2 = 1/4), otherwise nobody gets the white mouse, so according to the rule the dragon wins.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
 
public class Main1 {
	static PrintWriter out = new PrintWriter(System.out);
 
	static int a[], n;
	static boolean v[][];
	static double memo[][];
 
	static double solve2(int w, int b) {
		double selectBlack = 0;
		if (b > 0) {
			selectBlack = (((double) b) / (w + b));
			b--;
		}
 
		double jumpBlack = 0;
		double jumpWhite = 0;
 
		if (b > 0)
			jumpBlack = (((double) b) / (w + b));
		if (w > 0)
			jumpWhite = (((double) w) / (w + b));
 
		return selectBlack * (jumpBlack * solve(w, b - 1) + jumpWhite * solve(w - 1, b));
 
	}
 
	static double solve(int w, int b) {
		if (w <= 0 || b < 0) {
			return 0;
		}
		if (b == 0 && w > 0) {
			return 1;
		}
 
		if (v[w][b]) {
			return memo[w][b];
		}
 
		v[w][b] = true;
 
		double white = (((double) w) / (w + b));
		double black = (((double) b) / (w + b));
 
		return memo[w][b] = white + black * solve2(w, b - 1);
 
	}
 
	public static void main(String[] args) throws IOException {
		FastReader input = new FastReader();
 
		int w = input.nextInt();
		int b = input.nextInt();
		memo = new double[w + 1][b + 1];
		v = new boolean[w + 1][b + 1];
		out.println(solve(w, b));
		out.flush();
 
	}
 
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;
 
		public FastReader() {
			// try {
			// br = new BufferedReader(new FileReader(new File("input.txt")));
			// } catch (FileNotFoundException e) {
			// e.printStackTrace();
			// }
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() throws IOException {
			while (st == null || !st.hasMoreElements()) { st = new StringTokenizer(br.readLine()); }
			return st.nextToken();
		}
 
		int nextInt() throws NumberFormatException, IOException { return Integer.parseInt(next()); }
 
		long nextLong() throws NumberFormatException, IOException { return Long.parseLong(next()); }
 
		double nextDouble() throws NumberFormatException, IOException { return Double.parseDouble(next()); }
 
		String nextLine() throws IOException {
			String str = "";
			str = br.readLine();
			return str;
		}
 
		boolean hasNext() throws IOException { return br.ready(); }
	}
 
	static class con {
		static int IINF = (int) 1e9;
		static int _IINF = (int) -1e9;
		static long LINF = (long) 1e15;
		static long _LINF = (long) -1e15;
		static double EPS = 1e-9;
	}
 
	static class Triple implements Comparable<Triple> {
		int x;
		int y;
 
		int z;
 
		Triple(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}
 
		@Override
		public int compareTo(Triple o) {
			if (x == o.x && y == o.y)
				return z - o.z;
			if (x == o.x)
				return y - o.y;
			return x - o.x;
		}
 
		@Override
		public String toString() { return "(" + x + ", " + y + ", " + z + ")"; }
	}
 
	static class Pair implements Comparable<Pair> {
		int x;
		int y;
 
		Pair(int x, int y) {
			this.x = x;
			this.y = y;
 
		}
 
		@Override
		public int compareTo(Pair o) {
			if (x == o.x)
				return y - o.y;
			return x - o.x;
		}
 
		@Override
		public String toString() {
 
			return "(" + x + ", " + y + ")";
		}
 
	}
 
	static void shuffle(int[] a) {
		for (int i = 0; i < a.length; i++) {
			int r = i + (int) (Math.random() * (a.length - i));
			int tmp = a[r];
			a[r] = a[i];
			a[i] = tmp;
		}
	}
 
	static int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
 
	static class DSU {
 
		int[] p, rank, setSize;
		int numSets;
 
		DSU(int n) {
			p = new int[n];
			rank = new int[n];
			setSize = new int[n];
			numSets = n;
 
			for (int i = 0; i < n; i++) {
				p[i] = i;
				setSize[i] = 1;
			}
 
		}
 
		int findSet(int n) { return p[n] = p[n] == n ? n : findSet(p[n]); }
 
		boolean isSameSet(int n, int m) { return findSet(n) == findSet(m); }
 
		void mergeSet(int n, int m) {
 
			if (!isSameSet(n, m)) {
				numSets--;
				int p1 = findSet(n);
				int p2 = findSet(m);
 
				if (rank[p1] > rank[p2]) {
					p[p2] = p1;
					setSize[p1] += setSize[p2];
				} else {
					p[p1] = p2;
					setSize[p2] += setSize[p1];
					if (rank[p1] == rank[p2])
						rank[p1]++;
				}
			}
 
		}
 
		int size() { return numSets; }
 
		int setSize(int n) { return setSize[findSet(n)]; }
 
	}
 
	static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;
 
		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
 
		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
 
		public String readLine() throws IOException {
			byte[] buf = new byte[1024];
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}
 
		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do { ret = ret * 10 + c - '0'; } while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
 
		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do { ret = ret * 10 + c - '0'; } while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
 
		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do { ret = ret * 10 + c - '0'; } while ((c = read()) >= '0' && c <= '9');
			if (c == '.')
				while ((c = read()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);
			if (neg)
				return -ret;
			return ret;
		}
 
		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}
 
		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}
 
		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}
}