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: Wrong Answer)

#if 0

#endif

#include <bits/stdc++.h>
#define REP(i, n) for(int i=0;i<int(n);++i)
using namespace std;
template<class A>void p(A a){cout << (a) << endl;}
template<class A,class B>void p(A a,B b){cout << a << " "  ;p(b);}
template<class A,class B,class C>void p(A a,B b,C c){cout << a << " " ;p(b,c);}
template<class A,class B,class C,class D>void p(A a,B b,C c,D d){cout << a << " " ;p(b,c,d);}
typedef long long ll;
typedef pair<ll, ll> l_l;
typedef pair<int, int> i_i;
int INF=numeric_limits<int>::max();
// for copy
// for(int i=0;i<N;++i) {

int main(void) {
  int N,K;cin>>N>>K;
  double P = 0.0;
  for(int i=1;i<N+1;++i) {
    int t = log2(K/i) + 1;
    double tmp = 1.0/N;
    if(i<K) {
      tmp *= pow(0.5, t);
    }
    P += tmp;
  }
  printf("%.12f\n",P);
  return 0;
}