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 <iostream>
#include <vector>
#include <string>
#include <cstring>
#include <math.h>
#include <cmath>
#include <limits.h>
#include <map>
#include <unordered_map>
#include <set>
#include <queue>
#include <algorithm>
#include <functional>
#include <stdio.h>
using namespace std;

long long MOD = 1000000007;

//全体  
long long func1( long long l ) {
    if ( l == 0 ) { return 1; }
    else {
        long long ret = 1;
        while ( l > 0 ) {
            ret *= 2;
            ret += 3;
            l--;
        }
        return ret;
    }
}


//P
long long func2( long long l ) {
    long long ret = func1(l);
    return (ret+1)/2;
}


long long func3( long long l, long long k ) {
    if ( k <= 1 ) { return 0; }

    long long s = func1(l);
    long long p = func2(l);
    
    if ( s == k ) { return p; }



    if ( (s+1)/2 == k ) { return func2(l-1)+1; }
    else if ( (s+1)/2 > k ) { return func3(l-1, k-1); }
    else if ( (s+1)/2 < k ) { return func2(l-1)+1+func3(l-1,k-(2+func1(l-1)) ); }
}


int main() {
    
    long long N;
    long long X;
    cin >> N >> X;

    if ( X <= 1 ) { cout << 0 << endl; return 0; }

    cout << func3( N, X ) << endl;

    return 0;
}