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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
double pow2(int n){
    int i,a;
    double ans=1;
    if(n>=0){
    for(i=0;i<n;i++)
    ans=ans*2;
    }
    if(n<0){
        a=-n;
    for(i=0;i<a;i++)
    ans=ans/2;
    }
    
    return(ans);
}


int main(void){
    int i;
    double N,K;
    double sum=0;
    scanf("%lf %lf",&N,&K);
  
   for(i=1;i<=N;i++){
       if((double)(K/i)<=1)
       sum+=(double)(1/N);
       
       if(1<(double)(K/i)&&(double)(K/i)<=2)
       sum+=(double)(pow2(-1)/N);
       
       if(2<(double)(K/i)&&(double)(K/i)<=4)
       sum+=(double)(pow2(-2)/N);
       
       if(4<(double)(K/i)&&(double)(K/i)<=8)
       sum+=(double)(pow2(-3)/N);
       
        if(8<(double)(K/i)&&(double)(K/i)<=16)
       sum+=(double)(pow2(-4)/N);
       
        if(16<(double)(K/i)&&(double)(K/i)<=32)
       sum+=(double)(pow2(-5)/N);
       
        if(32<(double)(K/i)&&(double)(K/i)<=64)
       sum+=(double)(pow2(-6)/N);
       
        if(64<(double)(K/i)&&(double)(K/i)<=128)
       sum+=(double)(pow2(-7)/N);
       
        if(128<(double)(K/i)&&(double)(K/i)<=256)
       sum+=(double)(pow2(-8)/N);
       
        if(256<(double)(K/i)&&(double)(K/i)<=512)
       sum+=(double)(pow2(-9)/N);
      
       if(512<(double)(K/i)&&(double)(K/i)<=1024)
       sum+=(double)(pow2(-10)/N);
       
       if(1024<(double)(K/i)&&(double)(K/i)<=2048)
       sum+=(double)(pow2(-11)/N);
       
       if(2048<(double)(K/i)&&(double)(K/i)<=4196)
       sum+=(double)(pow2(-12)/N);
       
       if(4196<(double)(K/i)&&(double)(K/i)<=8192)
       sum+=(double)(pow2(-13)/N);
       
       if(8192<(double)(K/i)&&(double)(K/i)<=16384)
       sum+=(double)(pow2(-14)/N);
       
       if(16384<(double)(K/i)&&(double)(K/i)<=32768)
       sum+=(double)(pow2(-15)/N);
       
       if(32768<(double)(K/i)&&(double)(K/i)<=65536)
       sum+=(double)(pow2(-16)/N);
       
       if(65536<(double)(K/i)&&(double)(K/i)<=131072)
       sum+=(double)(pow2(-17)/N);
   }
  
    printf("%.13f",sum);
    return(0);
}