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 <bits/stdc++.h>
#include <iostream>
#include <complex>
#include <sstream>
#include <string>
#include <algorithm>
#include <deque>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <vector>
#include <set>
#include <limits>
#include <cstdio>
#include <cctype>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <climits>
#include <iomanip>
#include <stack>
#include <bitset>

#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, j, k) for(int i = (int)(j); i < (int)(k); ++i)
#define ROF(i, j, k) for(int i = (int)(j); i >= (int)(k); --i)
#define FORLL(i, n, m) for(long long i = n; i < (long long)(m); i++)
#define SORT(v, n) sort(v, v+n)
#define REVERSE(v) reverse((v).begin(), (v).end())

using namespace std;
using ll = long long;
const ll MOD=1000000007LL;
typedef pair<int, int> P;

ll ADD(ll x, ll y) { return (x+y) % MOD; }
ll SUB(ll x, ll y) { return (x-y+MOD) % MOD; }
ll MUL(ll x, ll y) { return x*y % MOD; }
ll POW(ll x, ll e) { ll v=1; for(; e; x=MUL(x,x), e>>=1) if (e&1) v = MUL(v,x); return v; }
ll DIV(ll x, ll y) { /*assert(y%MOD!=0);*/ return MUL(x, POW(y, MOD-2)); }

template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}return 0;}
template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}return 0;}

int
main(void){  
  ios_base::sync_with_stdio(false);
  cin.tie(0);

  int n, k;
  cin >> n >> k;
  double dn = 0.0;
  dn += n;
  double ans = 0.0;
  cout << fixed;
  cout << setprecision(14);
  /*
  cerr << fixed;
  cerr << setprecision(14);
  */
  
  FOR(i,1,n+1){
    if(i >= k) ans += (double)(1/dn);
    else{
      double times = 0.0;
      int val = i;
      while(val<k){
	val *= 2;
	times++;
      }
      //cerr << times << endl;
      //cerr << (double)(1/dn) << endl;
      ans += (double)(1/dn) * (double)pow(0.5,times);
    }
  }
  cout << ans << endl;
  
  return 0;
}