Problem:
Score : 300 points

Problem Statement

Snuke has a fair N-sided die that shows the integers from 1 to N with equal probability and a fair coin. He will play the following game with them:

Throw the die. The current score is the result of the die.

As long as the score is between 1 and K-1 (inclusive), keep flipping the coin. The score is doubled each time the coin lands heads up, and the score becomes 0 if the coin lands tails up.

The game ends when the score becomes 0 or becomes K or above. Snuke wins if the score is K or above, and loses if the score is 0.

You are given N and K. Find the probability that Snuke wins the game.

Constraints

1 ≤ N ≤ 10^5

1 ≤ K ≤ 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the probability that Snuke wins the game. The output is considered correct when the absolute or relative error is at most 10^{-9}.

Sample Input 1

3 10

Sample Output 1

0.145833333333

If the die shows 1, Snuke needs to get four consecutive heads from four coin flips to obtain a score of 10 or above. The probability of this happening is \frac{1}{3} \times (\frac{1}{2})^4 = \frac{1}{48}.

If the die shows 2, Snuke needs to get three consecutive heads from three coin flips to obtain a score of 10 or above. The probability of this happening is \frac{1}{3} \times (\frac{1}{2})^3 = \frac{1}{24}.

If the die shows 3, Snuke needs to get two consecutive heads from two coin flips to obtain a score of 10 or above. The probability of this happening is \frac{1}{3} \times (\frac{1}{2})^2 = \frac{1}{12}.

Thus, the probability that Snuke wins is \frac{1}{48} + \frac{1}{24} + \frac{1}{12} = \frac{7}{48} \simeq 0.1458333333.

Sample Input 2

100000 5

Sample Output 2

0.999973749998

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

/*
......................................................................................................................................
.....................................  ________ ____ __________________________________________ .....................................
..................................... /  _____/|    |   \      \__    ___/\_   _____/\______   \.....................................
...................................../   \  ___|    |   /   |   \|    |    |    __)_  |       _/.....................................
.....................................\    \_\  \    |  /    |    \    |    |        \ |    |   \.....................................
..................................... \______  /______/\____|__  /____|   /_______  / |____|_  /.....................................
.....................................        \/                \/                 \/         \/ .....................................
......................................................................................................................................
.............................................................,;'';:...................................................................
........................................................+@@@@@@@@@@@@@@'..............................................................
.....................................................#@@@##############@@@:...........................................................
...................................................@@@####################@@,.........................................................
.................................................@@#########################@@........................................................
...............................................:@############################@@.......................................................
..............................................@@######@@@#';;'#@@@############@@:.....................................................
.............................................@#####@@,````````````,@@###########@:....................................................
............................................@####@;``````````````````+@##########@....................................................
...........................................@###@:``````````````````````#@########@@...................................................
..........................................@####``````````````````````````@########@@..................................................
.........................................###@.````````````````````````````@########@+.................................................
.........................................@#@```````````````````````````````#########@.................................................
........................................@#@`````````````````````````````````########@@................................................
.......................................,@@```````````````````````````````````@#######@:...............................................
.......................................@@`````````````````````````````````````@#######@...............................................
.......................................@:````````````````````#@@'``````````````@######@+..............................................
......................................#@```````````````````@@@@@@@#````````````########@..............................................
......................................@```````````````````@@@@@@@@@@````````````@######@+.............................................
......................................@``````````````````@@@@@@@+   +```````````+#######@.............................................
.....................................;:``````````````````@@@@@@@    @````````````@######@'............................................
.....................................@``````````````````:@@@@@@@    @````````````@#######@............................................
.....................................@```,@@@#``````````;@@@@@@@    @````````````:#######@:...........................................
.....................................@``@@@@@@@@````````.@@@@@@@#  ,#`````````````@#######@...........................................
.....................................@`@@@@@@@+'@````````@@@@@@@@@@@``````````````@#######@...........................................
.....................................@,@@@@@@   ,```:+:``:@@@@@@@@@.``````````````@########@..........................................
.....................................#@@@@@@@  ;@@#;,,,@``:@@@@@@@````````````````#########@..........................................
.....................................+@@@@@@@@',,,,,,,,;,```.'+;``````````````````'########@;.........................................
.....................................'@@@@',,,,,,,,,,,,,@`````````````````````````:#########@.........................................
....................................:@#,,,,,:;;;;;:,,,,,@`````````````````````````.#########@.........................................
.................................:@#@@@@#++';;;;;;;;;;;;@``````````````````````````##########+........................................
...............................#@#+;;;;;;;;;;;;;;;;;;;;':``````````````````````````##########@........................................
....................................,@#@@@@@#+'';;;;;+@#```````````````````````````##########@........................................
.....................................@``````````.,,,.``````````````````````````````############.......................................
.....................................@`````````````````````````````````````````````#######+'+#@.......................................
.....................................@`````````````````````````````````````````````##########'@.......................................
.....................................#`````````````````````````````````````````````############@#.....................................
.....................................:.````````````````````````````````````````````##############@,...................................
......................................+```````````````````````````````````````````.###############@#..................................
......................................@```````````````````````````````````````````.################@@.................................
......................................@```````````````````````````````````````````.###+##############@................................
......................................@```````````````````````````````````````````.###+###############@...............................
......................................',``````````````````````````````````````````.####'##############@@..............................
.......................................@```````````````````````````````````````````#####+##############@:.............................
.......................................@```````````````````````````````````````````#####'###############@.............................
.......................................@```````````````````````````````````````````######'################............................
.......................................#,``````````````````````````````````````````#######'##############@............................
........................................@``````````````````````````````````````````@######++##############+...........................
........................................@``````````````````````````````````````````@#######'##############@...........................
........................................@``````````````````````````````````````````@########'#############@...........................
.......................................@#'`````````````````````````````````````````@#########'##############..........................
.......................................@#@`````````````````````````````````````````+#########+'############@..........................
......................................@##@`````````````````````````````````````````.##########+'###########@..........................
......................................@##@:`````````````````````````````````````````###########+'###########..........................
.....................................:@###@`````````````````````````````````````````@###########+'+#########,.........................
.....................................@####@`````````````````````````````````````````@#############''########..........................
.....................................@####@.````````````````````````````````````````;##############+'######@..........................
.....................................@#####@`````````````````````````````````````````################@@@###+..........................
.....................................@#####@`````````````````````````````````````````@###############@..;;............................
....................................,@#####@.````````````````````````````````````````+################'...............................
....................................:#######@`````````````````````````````````````````################@...............................
....................................:#######@`````````````````````````````````````````@###############@...............................
....................................,@#######,````````````````````````````````````````:###############@...............................
.....................................@######@@`````````````````````````````````````````@##############@...............................
.....................................@######@@`````````````````````````````````````````+##############@...............................
.....................................@#####@,;;`````````````````````````````````````````@#############@...............................
.....................................@####@@..@`````````````````````````````````````````+#############@...............................
.....................................,####@...@``````````````````````````````````````````@############+...............................
......................................@##@.....@`````````````````````````````````````````:###########@,...............................
.......................................@+......@``````````````````````````````````````````@##########@................................
...............................................:#``````````````````````````````````````````##########@................................
................................................@``````````````````````````````````````````+########@,................................
................................................'+``````````````````````````````````````````@#######@.................................
.................................................@```````````````````````````````````````````@#####@:.................................
.................................................'#``````````````````````````````````````````.#####@..................................
..................................................@```````````````````````````````````````````;###@...................................
...................................................@```````````````````````````````````````````+#@'...................................
...................................................'#```````````````````````````````````````````@#....................................
....................................................##`````````````````````````````````````````@#.....................................
.....................................................#@```````````````````````````````````````@+......................................
......................................................:@;```````````````````````````````````;@,.......................................
.......................................................;@@'```````````````````````````````:@@+;.......................................
.......................................................@,,'@@'``````````````````````````@@@,,,@.......................................
......................................................@,,,,,,'@@@@;````````````````.+@@@;,,,,,@.......................................
......................................................#@+@,,,,,,,,+@@@@@@@@@@@@@@@@@;,,,,,'@@@........................................
.........................................................+,,,#',,@@..............@,,,,,,,,@...........................................
..........................................................@@@,#@@,...............:+,,,'@,,@...........................................
..................................................................................@,,,@.##............................................
...................................................................................@;@................................................
....................................................................................:.................................................
......................................................................................................................................
......................................................................................................................................
 */

import javax.swing.text.DateFormatter;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.time.LocalDate;
import java.time.format.DateTimeFormatter;
import java.util.*;
import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;

import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.pow;
import static java.lang.Math.abs;

import static java.lang.String.format;


public class Main {
    final static int INF = Integer.MAX_VALUE>>1;
    final static int MOD = 1_000_000_007;
    final static int[] dx4 = { 0, 1, 0, -1 };
    final static int[] dy4 = { 1, 0, -1, 0 };
    final static int[] dx8 = {0, 1, 1,  1,  0, -1, -1, -1};
    final static int[] dy8 = {1, 1, 0, -1, -1, -1, 0, 1};
    public static void main(String[] args) {
        Scanner sc=new Scanner();
        int n = sc.nextInt();
        int k = sc.nextInt();
        int nn=min(n,k-1);
        BigDecimal bd=new BigDecimal(max(0.0,n-k+1)/n);
        putE(bd);
        for (int i = 1; i <= nn; i++) {
            double lose=0;
            int cnt=0;
            while(i*(1<<cnt)<k){
                lose+=Math.pow(1/2.0,(cnt++)+1);
            }
            bd=bd.add(new BigDecimal((1-lose)/n));
        }
        put(bd);

    }



    public static void print(Object object){
        System.out.print(object);
    }
    public static void put(Object object) {
        System.out.println(object);
    }
    public static void put(){
        System.out.println();
    }

    public static void printE(Object object){
        System.err.print("DEBUG:"+object);
    }
    public static void putE(Object object){
        System.err.println("DEBUG:"+object);
    }
    public static void putE(){
        System.err.println("DEBUG:");
    }

    public static void print(String format,Object... args){
        System.out.print(String.format(format,args));
    }
    public static void put(String format,Object... args) {
        System.out.println(String.format(format,args));
    }
    public static void printE(String format,Object... args){
        System.err.print("DEBUG:"+String.format(format,args));
    }
    public static void putE(String format,Object... args){
        System.err.println("DEBUG:"+String.format(format,args));
    }

    final static private class Scanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte())
                return buffer[ptr++];
            else
                return -1;
        }

        private boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr]))
                ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
                throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
    final static private class FixedIntPair {
        final public int x, y;
        final static public FixedIntPair ZEROS=new FixedIntPair(0,0);
        FixedIntPair(int x, int y) {
            this.x = x;
            this.y = y;
        }
        public static double distance(FixedIntPair fip1,FixedIntPair fip2){
            double x = (double) fip1.x - fip2.x;
            double y = (double) fip1.y - fip2.y;
            return Math.sqrt(x*x+y*y);
        }

        @Override
        public int hashCode() {
            return x+y;
        }

        @Override
        public boolean equals(Object obj) {
            if(obj==null)return false;
            if(!(obj instanceof FixedIntPair)) return false;
            FixedIntPair pair=(FixedIntPair) obj;
            return this.x==pair.x&&this.y==pair.y;
        }

        @Override
        public String toString() {
            return String.format(FixedIntPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class FixedLongPair {
        final public long x, y;
        final static public FixedLongPair ZEROS=new FixedLongPair(0,0);
        FixedLongPair(long x, long y) {
            this.x = x;
            this.y = y;
        }
        public static double distance(FixedLongPair flp1,FixedLongPair flp2){
            double x = (double) flp1.x - flp2.x;
            double y = (double) flp1.y - flp2.y;
            return Math.sqrt(x*x+y*y);
        }

        @Override
        public int hashCode() {
            return (int)x+(int)y;
        }

        @Override
        public boolean equals(Object obj) {
            if(obj==null)return false;
            if(!(obj instanceof FixedLongPair)) return false;
            FixedLongPair pair=(FixedLongPair)obj;
            return this.x==pair.x&&this.y==pair.y;
        }

        @Override
        public String toString() {
            return String.format(FixedLongPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class Binary{
        public static String toZeroPadding(int i){
            return String.format("%"+Integer.toBinaryString(-1).length()+"s",Integer.toBinaryString(i)).replace(' ','0');
        }
        public static String toZeroPadding(long i){
            return String.format("%"+Long.toBinaryString(-1).length()+"s",Long.toBinaryString(i)).replace(' ','0');
        }
    }

    final static private class Util {
        static long gcd(long a,long b){
            a=Math.abs(a);
            b=Math.abs(b);
            if(a<b){
                long tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                long r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static int gcd(int a,int b){
            a=Math.abs(a);
            b=Math.abs(b);
            if(a<b){
                int tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                int r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static long lcm(long a,long b){
            long gcd=gcd(a,b);
            long result=b/gcd;
            return a*result;
        }
        static boolean isValidCell(int i,int j,int h,int w){
            return i>=0&&i<h&&j>=0&&j<w;
        }
    }
}