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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

long long l[100];

void layer(int n) {
    int i;
    l[0] = 1;
    for (i=1;i<=n;i++) l[i] = l[i-1]*2 + 3;
}

long long burger(int n, long long c) {
    if (n == 0) return 1;
    else {
        if (c == 1) return 0;
        else if (c == l[n]) return 2*burger(n-1,l[n-1])+1;
        else if (c == (l[n]+1)/2) return burger(n-1,l[n-1])+1;
        else if (c < (l[n]+1)/2) return burger(n-1,c-1);
        else return burger(n-1,l[n-1])+1+burger(n-1,c-2-l[n-1]);
    }
}

int main(void) {
    int N;
    long long X;
    scanf("%d%lld", &N, &X);
    
    layer(N);
    printf("%lld\n", burger(N, X));

    return 0;
}