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++ (GCC 9.2.1) (judge verdict: Accepted)

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

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

#define rep(i,cc,n) for(int i=cc;i<n;++i)
#define lrep(i,cc,n) for(long long i=cc;i<n;++i)
#define sqrep(i,cc,n) for(long long i=cc;i*i<=n;++i)
#define rrep(i,cc,n) for(long i=cc;i>n;--i)
#define pii pair<int, int>
#define pll pair<long long, long long>
 
using ll = long long;

const vector<int> dx = {1, 0, -1, 0};
const vector<int> dy = {0, 1, 0, -1};
const double PI = 3.1415926535;
const ll inf = 1001001001;
const ll e9  = 1000000000;
const ll mod = 1000000007;

ll solve(int n, ll x){
    if(n==0)return 1;
    ll len = (1LL<<(n+1))-3;
    ll bnum = (1LL<<n)-1;
    if(x==1)return 0;
    else if(x<=len+1)return solve(n-1, x-1);
    else if(x==len+2)return bnum+1;
    else if(x<=len*2+2)return bnum+1+solve(n-1, x-len-2);
    else return bnum*2+1;
}
int main(){
    int n;
    ll x;
    cin >> n >> x;
    cout << solve(n, x);
    return 0;
}