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: Accepted)

#include<iostream>
using namespace std;

typedef unsigned long long ull;

ull len[51];
ull p_num_list[51];

ull calc_len(int n){
    if(n==0){
        len[n] = 1;
        return 1;
    }
    else{
        ull l = calc_len(n-1)*2+3;
        len[n] = l;
        return l;
    }
}

ull calc_p_num(int n){
    if(n==0){
        p_num_list[n] = 1;
        return 1;
    }
    else{
        ull l = calc_p_num(n-1)*2+1;
        p_num_list[n] = l;
        return l;
    }
}


ull func(int n, ull x){
    if(n==1){
        if(x==1)
          return 0;
        else if(x <= 4)
          return x-1;
        else
          return 3;
    }

    if(x <= 1){
        return 0;
    }
    else{
        x--;
        ull res = 0;
        if(x <=len[n-1]){
            //cout << n << ", " << x << " : test1" << endl;
            return func(n-1, x);
        }
        else if(x == len[n-1]+1){
            //cout << n << ", " << x << " : test2" << endl;
            return p_num_list[n-1] + 1;
        }
        else{
            x = x - len[n-1]-1;
            //cout << n << ", " << x << " : test3" << endl;
            return func(n-1, min(x, len[n-1])) + 1 + p_num_list[n-1];
        }
    }
}


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

    calc_len(50);
    for(int i=0;i<=50;i++){
        //cout << len[i] << endl;
    }

    calc_p_num(50);
    for(int i=0;i<=50;i++){
        //cout << p_num_list[i] << endl;
    }

    ull ans = func(N, X);
    cout << ans << endl;
    return 0;
}