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++14 (GCC 5.4.1) (judge verdict: Accepted)

//INCLUDE
//------------------------------------------
#include <bits/stdc++.h>
//DEFINE
//------------------------------------------
#define ll long long
#define ld long double
#define ALLv(a)  (a).begin(),(a).end()
#define ALL(a,n)  (a),(a)+n
#define vi vector<long long>
#define vd vector<long double>
#define vs vector<string>
//CONST
//------------------------------------------
#define INF 1010000000000000017LL
#define MOD 1000000007LL
#define EPS 1e-12
#define PI 3.14159265358979323846
//REPEAT
//------------------------------------------
#define   FOR(i,m,n) for(ll (i)=(m);   (i)<(n);  (i)++)
#define   REP(i,n)   for(ll (i)=0;     (i)<(n);  (i)++)
#define  REPS(i,x)   for(ll (i)=1;     (i)<=(x); (i)++)
#define  RREP(i,x)   for(ll (i)=(x)-1; (i)>=0;   (i)--)
#define RREPS(i,x)   for(ll (i)=(x);   (i)> 0;   (i)--)
#define  WREP(i,in,j,jn) REP(i,in)REP(j,jn)
//-----------------------------------------
#define dcml(n) fixed<<setprecision(n)
using namespace std;
int main(void){
    ll N,K;cin>>N>>K;
    ld ans=0;
    REPS(i,N){//さいころの面
        ll point=i;
        ld p=1.0/N;
        while(point<K){
            p/=2;
            point*=2;
        }
        ans+=p;
    }
    cout<<dcml(15)<<ans<<"\n";
}