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>
#include <limits.h>
#include <algorithm>
#include <math.h>
using namespace std;

long long a(int n) {
    return pow(2, n + 2) - 3;
}
long long p(int n) {
    return pow(2, n + 1) - 1;
}

int main(void){
    long long n, x;
    cin >> n >> x;
    
    long long k, ans = 0;
    while (x > 0) {
        k = 0;
        while (a(k + 1) + n - k - 1 <= x) k++;
        if (k == 0) {
            if (x > n) ans += x - n;
            break;
        }
        
        ans += p(k);
        x -= a(k) + n - k;
        
        if (x > 0) {
            ans++;
            x--;
        }
        
        n = k;
    }
    
    cout << ans << endl;
}