Problem:
Score : 400 points

Problem Statement

In some other world, today is Christmas.

Mr. Takaha decides to make a multi-dimensional burger in his party. A level-L burger (L is an integer greater than or equal to 0) is the following thing:

A level-0 burger is a patty.

A level-L burger (L \geq 1) is a bun, a level-(L-1) burger, a patty, another level-(L-1) burger and another bun, stacked vertically in this order from the bottom.

For example, a level-1 burger and a level-2 burger look like BPPPB and BBPPPBPBPPPBB (rotated 90 degrees), where B and P stands for a bun and a patty.

The burger Mr. Takaha will make is a level-N burger. Lunlun the Dachshund will eat X layers from the bottom of this burger (a layer is a patty or a bun). How many patties will she eat?

Constraints

1 \leq N \leq 50

1 \leq X \leq ( the total number of layers in a level-N burger )

N and X are integers.

Input

Input is given from Standard Input in the following format:

N X

Output

Print the number of patties in the bottom-most X layers from the bottom of a level-N burger.

Sample Input 1

2 7

Sample Output 1

4

There are 4 patties in the bottom-most 7 layers of a level-2 burger (BBPPPBPBPPPBB).

Sample Input 2

1 1

Sample Output 2

0

The bottom-most layer of a level-1 burger is a bun.

Sample Input 3

50 4321098765432109

Sample Output 3

2160549382716056

A level-50 burger is rather thick, to the extent that the number of its layers does not fit into a 32-bit integer.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<utility>
#include<algorithm> // sort
#include<map> // pair
#include<cmath>
#include<cstring>
#include<set>
using namespace std;
using ll = long long;
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; }
#define rep(i, n) REP(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define MSG(a) cout << #a << " " << a << endl;
#define REP(i, x, n) for(int i = x; i < n; i++)
#define all(x) (x).begin(),(x).end()
const ll mod = 1e9+7;
const int INF = 1e9;
const ll INFLONG = 1e18;
ll sum;
ll x;
int main(){
  ll n;
  cin >> n >> x;
  ll a[n+1];//the number of p
  ll b[n+1];//the number of all
  a[0] = 1;
  b[0] = 1;
  rep(i,n){
    a[i+1] = a[i]*2+1;
    b[i+1] = b[i]*2+3;
  }
  sum = 0;
  for(int i=n;i>=0;i--){
    if(x >= b[i]){
      if(x > b[i]){
        sum++;
        x--;
      }
      sum += a[i];
      x -= b[i];
      //cout << sum << " " << x << " " << i <<  endl;
      i++;
    }else{
      x--;
    }
  }
  cout << sum;
}