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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;

#define ll long long
#define ld long double
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define lb lower_bound
#define ub upper_bound
#define loop(i,a,b) for(ll i=a;i<b;i++)
#define initialize(array,size,value) for(ll i=0;i<size;i++) array[i]=value
#define couta(array,size) for(ll i=0;i<size;i++) cout<<array[i]<<" "
#define inf (long long int) 1e18
#define eps 0.000001
#define vl vector<ll> 
#define sl set<ll>
#define pll pair<ll, ll>
#define mll map<ll, ll> 
#define pq priority_queue<ll>
#define mod 1000000007
#define MAXN 100001
ll spf[MAXN]; 
ll gcd(ll a,ll b);
ll palindrome(string s);
ll modexp(ll a,ll b,ll m);
void sieve();
ll ceil(ll a, ll b);
vl getFactorization(ll x);
void getZarr(string str, ll Z[]);
vector<ll> prefix_function(string s);
 
vector<pll> adj[100005];
bool vis[100005];
void dfs(ll s){
    vis[s]=true;
    for(auto x: adj[s]){
        ll weigh=x.se , neigh=x.fi;
        if(vis[neigh]==false && weigh==0){
            dfs(neigh);
        }
    }
}

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0);
    /*#ifndef ONLINE_JUDGE
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif*/

    ll n,x;
    cin>>n>>x;
    ll dp[n+1];
    dp[0]=1;
    for(ll i=1;i<n+1;i++){
        dp[i]=2*dp[i-1]+3;
    }
    /*loop(i,0,n+1){
        //cout<<"i: "<<i<<endl;
        cout<<dp[i]<<endl;
    }*/
    vector<ll> v[n+1];
    v[0].pb(0);
    loop(i,1,n+1){
        for(auto x:v[i-1]){
            v[i].pb(x+1);
        }
        v[i].pb(dp[i]/2);
        reverse(v[i-1].begin(), v[i-1].end());
        for(auto x:v[i-1]){
            v[i].pb(dp[i]-1-(x+1));
        }
        reverse(v[i-1].begin(), v[i-1].end());
    }
    //for(auto x:v[n]) cout<<x<<" ";
    ll ab=lb(v[n].begin(), v[n].end(),x)-v[n].begin();
    cout<<ab<<endl;
}
ll gcd(ll a, ll b){
    if (a == 0)   return b;
    if(b==0)      return a;
    if (a == b)   return a;
    if (a > b)    return gcd(a%b, b);
    return gcd(a, b%a);
}

ll palindrome(string s){
    ll l = 0;
    ll h = s.length() - 1;
    while (h > l){
        if (s[l++] != s[h--]){
            return 0;
        }
    }
    return 1;
}

ll modexp(ll a, ll b, ll m){
    if (b==0)
        return 1;
    ll temp = modexp(a,b/2,m);
    temp = (temp*temp)%m;
    if (b&1)
        return (temp*(a%m))%m; // if b is odd a^b = a^(b/2)*a^(b/2)*a
    return temp;
}

void sieve() { 
    spf[1] = 1; 
    for (ll i=2; i<MAXN; i++) 
        spf[i] = i; 
    for (ll i=4; i<MAXN; i+=2) 
        spf[i] = 2; 
  
    for (ll i=3; i*i<MAXN; i++) { 
        if (spf[i] == i) { 
            for (ll j=i*i; j<MAXN; j+=i) 
                if (spf[j]==j) 
                    spf[j] = i; 
        } 
    } 
} 

vl getFactorization(ll x) 
{ 
    vl ret; 
    while (x != 1) 
    { 
        ret.push_back(spf[x]); 
        x = x / spf[x]; 
    } 
    return ret; 
} 

ll ceil(ll a,ll b){
    return a/b+(a%b!=0);
}

void getZarr(string str, ll Z[]){
    ll n = str.length();
    ll L, R, k;
    L = R = 0;
    for (ll i = 1; i < n; ++i){
        if (i > R){
            L = R = i;
            while (R<n && str[R-L] == str[R])
                R++;
            Z[i] = R-L;
            R--;
        } else {
            k = i-L;
            if (Z[k] < R-i+1)
                Z[i] = Z[k];
            else {
                L = i;
                while (R<n && str[R-L] == str[R])
                    R++;
                Z[i] = R-L;
                R--;
            }
        }
    }
}

vector<ll> prefix_function(string s) {
    ll n = (ll)s.length();
    vector<ll> pi(n);
    for (ll i = 1; i < n; i++) {
        ll j = pi[i-1];
        while (j > 0 && s[i] != s[j])
            j = pi[j-1];
        if (s[i] == s[j])
            j++;
        pi[i] = j;
    }
    return pi;
}