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++ (Clang 10.0.0) (judge verdict: Accepted)

//#pragma GCC optimize ("O3","unroll-loops")
#include<iostream>
#include<iomanip>
#include<cstdio>
#include<cstdlib>
#include<cassert>

#include<cmath>
#include<functional>
#include<algorithm>
#include<numeric>

#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<deque>
#include<set>
#include<map>
#include<bitset>
#include<tuple>

#define TEST {IS_TEST=true;}
#define fi first
#define se second
#define pb(x) emplace_back(x)
#define pf(x) emplace_front(x)
#define emp(x) emplace(x)
#define mp(x,y) make_pair(x,y)

using namespace std;
using ll = int_fast64_t;
using v_b = vector <bool>; using v_ll = vector <ll>; using str = string; using v_str = vector <string>; using p_ll = pair < ll,ll >;
using vv_b = vector < v_b >; using vv_ll = vector < v_ll >; using vp_ll = vector < p_ll >;
using vvv_ll = vector < vv_ll >; using vvp_ll = vector < vp_ll >;
using ld = long double; using v_ld = vector <ld>; using vv_ld = vector<v_ld>;

bool IS_TEST=false;
ll ll_min64=1LL<<63;
ll ll_max64=~ll_min64;
ll ll_min32=1LL<<31;
ll ll_max32=~ll_min32;

ll MOD = 1000000007;

/*displaying functions for debug*/
template<class T> void show2(const T &x){cerr << x;}
template<class T1,class T2> void show2(const pair<T1,T2> &x){
  cerr << "{" << show2(x.first) << "," << show2(x.second) << "}";
}
template<class T> void show(const T &x){
  if (!IS_TEST) return; show2(x); cerr << "\n";
}
template<class T> void v_show(const T &v, ll n=-1){
  if (!IS_TEST) return; auto itr=v.begin(); ll m=n;
  while(itr!=v.end() && m!=0 ){ show2(*itr); cerr << " "; itr++; m--;}
  cerr << "\n";
}
template<class T> void vv_show(const T &v, ll n=-1){
  if (!IS_TEST) return;
  cerr << "--------------------------------\n";
  auto itr=v.begin(); ll m=n;
  while(itr!=v.end() && m!=0 ){ v_show(*itr,n); itr++; m--;}
  cerr << "--------------------------------\n";
}
/*--------------------------------*/

/*loading integers*/
void load(ll& x1){ cin >> x1; }
void load(ll& x1,ll& x2){ cin >> x1 >> x2; }
void load(ll& x1,ll& x2,ll& x3){ cin >> x1 >> x2 >> x3; }
void load(ll& x1,ll& x2,ll& x3,ll& x4){ cin >> x1 >> x2 >> x3 >> x4; }
void v_load(ll n, v_ll& v1, ll head=0, ll tail=0, ll init=0){
    ll m=n+head+tail; v1.assign(m,init);
    for (ll i=0;i<n;i++){ scanf("%lld",&v1[i+head]); }
}
void v_load(ll n, v_ll& v1 ,v_ll& v2, ll head=0, ll tail=0, ll init=0){
    ll m=n+head+tail; v1.assign(m,init); v2.assign(m,init);
    for (ll i=0;i<n;i++){ scanf("%lld%lld",&v1[i+head],&v2[i+head]); }
}
void v_load(ll n, v_ll& v1 ,v_ll& v2, v_ll& v3, ll head=0, ll tail=0, ll init=0){
    ll m=n+head+tail; v1.assign(m,init); v2.assign(m,init); v3.assign(m,init);
    for (ll i=0;i<n;i++){ scanf("%lld%lld%lld",&v1[i+head],&v2[i+head],&v3[i+head]); }
}
void v_load(ll n, v_ll& v1 ,v_ll& v2, v_ll& v3, v_ll& v4, ll head=0, ll tail=0, ll init=0){
    ll m=n+head+tail; v1.assign(m,init); v2.assign(m,init); v3.assign(m,init); v4.assign(m,init);
    for (ll i=0;i<n;i++){ scanf("%lld%lld%lld%lld",&v1[i+head],&v2[i+head],&v3[i+head],&v4[i+head]); }
}
/*--------------------------------*/

v_ll local_sort(ll x1=ll_max64, ll x2=ll_max64, ll x3=ll_max64, ll x4=ll_max64){
    v_ll x{x1,x2,x3,x4};
    sort(x.begin(),x.end());
    return x;
}

ll max(ll x,ll y){return x>y?x:y;}
ll min(ll x,ll y){return x<y?x:y;}

ll max(v_ll::iterator b,v_ll::iterator e){
    ll ans=*b;
    while (b<e) {ans=max(ans,*b);b++;}
    return ans;
}
ll argmax(v_ll::iterator b,v_ll::iterator e){
    ll ans=0, cnt=0, val=*b;
    while (b<e) { if (val<*b) {ans=cnt; val=*b;} cnt++; b++;}
    return ans;
}
ll min(v_ll::iterator b,v_ll::iterator e){
    ll ans=*b;
    while (b<e) {ans=min(ans,*b);b++;}
    return ans;
}
ll argmin(v_ll::iterator b,v_ll::iterator e){
    ll ans=0, cnt=0, val=*b;
    while (b<e) { if (val>*b) {ans=cnt; val=*b;} cnt++; b++;}
    return ans;
}
ll sum(v_ll::iterator b,v_ll::iterator e){
    ll ans=0;
    while (b<e) {ans+=*b;b++;}
    return ans;
}

template<class T> bool chmax(T& x,const T& y){ if (x>=y) return false; x=y; return true;}
template<class T> bool chmin(T& x,const T& y){ if (x<=y) return false; x=y; return true;}

template<class T> void quit(T x){cout << x << endl; exit(0);}
void yesno(bool x){cout << (x?"Yes":"No") <<endl;}

ll rup(ll x,ll y){return (x-1)/y+1;}
ll rem(ll x,ll y){ ll z=x%y; return z>=0?z:z+y; }

template<typename T>
v_ll index_sort(const vector<T>& ref){
    v_ll idx(ref.size());
    iota(idx.begin(),idx.end(),0);
    sort(idx.begin(),idx.end(),[&](auto &x, auto &y){if (ref[x]<ref[y]) return true;});
}

//setprecision(digit)
//sort(##.begin(),##.end(),[&](auto &x, auto &y){if (x<y) return true;});
//ll ok=0,ng=0; while(abs(ok-ng)>1){ll mid=(ok+ng)/2; (true?ok:ng)=mid;}

struct dat{
    dat(){}
    bool operator < (const dat& rhs)const {return false; }
};

int main(){
    ll N,X;
    cin >> N >> X;
    v_ll layer(51,0);
    v_ll patty(51,0);
    for(ll i=0;i<=50;i++){
        layer[i]=(1LL<<(i+2))-3;
        patty[i]=(1LL<<(i+1))-1;
    }

    ll ans=0;
    for(ll i=N;i>=0;i--){
        if (X==0) break;
        if (i==0){
            ans++;
        }
        else if (X<=1){
            break;
        }
        else if (X==layer[i]){
            ans+=patty[i];
            break;
        }
        else if (X==2+layer[i-1]){
            ans++;
            ans+=patty[i-1];
            break;
        }
        else if (2<=X && X<=1+layer[i-1]){
            X--;
        }
        else if (3+layer[i-1]<=X && X<=layer[i]-1){
            ans++;
            ans+=patty[i-1];
            X-=2+layer[i-1];
        }
    }
    cout << ans << endl;
}