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"
using namespace std;
typedef long long ll;
#define int ll
typedef pair<int,int> pii;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define all(a) (a).begin(),(a).end()
#define pb emplace_back

int dfa[51]={};
int fa(int n){
    if(dfa[n]!=0)return dfa[n];
    if(n==1)return 1;
    else return dfa[n] = fa(n-1)*2+3;
}

int dfp[51]={};
int fp(int n){
    if(dfp[n]!=0)return dfp[n];
    if(n==1)return 1;
    else return dfp[n] = fp(n-1)*2+1;
}

signed main(){
    int n,x;
    cin>>n>>x;

    int ans = 0;
    while(x>0){
        for(int i=n;i>=0;i--){
            if(x>=fa(i)){
                x-=fa(i);
                ans+=fp(i);

                if(x>0){
                    x--;
                    ans++;
                }

                n = i;
                break;
            }else{
                x--;
            }
        }
    }

    cout<<ans<<endl;
}