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: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i,a,b) for(ll i=ll(a);i<ll(b);i++)
#define irep(i,a,b) for(ll i=ll(a);i>=ll(b);i--)
#define pb push_back
#define mp make_pair
#define pll pair<ll,ll>
#define F .first
#define S .second 
using ll=long long;
using ld=long double;
using namespace std;
const ll mod=1e9+7;
ll funca(ll n){
  if(n==0)return 1;
  else return funca(n-1)*2+3;
}
ll funcp(ll n){
  if(n==0)return 1;
  else return funcp(n-1)*2+1;
}
ll funcans(ll n,ll x){
  if(x<2)return 0;
  else if(x>1&&x<=funca(n-1)+1)return funcans(n-1,x-1);
  else return funcp(n-1)+1+funcans(n-1,x-2-funca(n-1));
}
main(){
  ll n,x;
  cin>>n>>x;
  cout<<funcans(n,x);
}