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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>

long long N, X;
long long layer[51], patty[51];

long long get_layer (int level)
{
    if (level == 0) return 1;
    return get_layer(level - 1) * 2 + 3;
}

long long get_patty (int level)
{
    if (level == 0) return 1;
    return get_patty(level - 1) * 2 + 1;
}

long long eat_runrun (int level, long long x)
{
    if (level == 1) {
        if (x == 5)  return 3;
        if (x == 4) return 3;
        if (x == 3) return 2;
        if (x == 2) return 1;
        return 0;
    }
    if (x == (layer[level] + 1) / 2) return patty[level - 1] + 1;
    else if (x < (layer[level] + 1) / 2) return eat_runrun(level - 1, x - 1);
    else return patty[level - 1] + 1 + eat_runrun(level - 1, x - (layer[level] + 1) / 2);
}

int main (void)
{
    int i;

    scanf("%lld %lld", &N, &X);

    for (i = 0; i < 51; i++) {
        layer[i] = get_layer(i);
        patty[i] = get_patty(i);
    }

    printf("%lld\n", eat_runrun(N, X));

    return 0;

}