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 "bits/stdc++.h"
using namespace std;
long long a[51], b[51];
long long layer(long long x)
{
	if(!a[x])
	{
		a[x] = 1 + layer(x - 1) + 1 + layer(x - 1) + 1;
	}
	return a[x];
}
long long patty(long long x)
{
	if(!b[x])
	{
		b[x] = patty(x - 1) + 1 + patty(x - 1);
	}
	return b[x];
}
int main()
{
	a[0] = 1;
	b[0] = 1;
	long long n, x, total = 0;
	scanf("%lld%lld", &n, &x);
	for(long long i = 0, j = n; i < x && j >= 0; )
	{
		if(i + layer(j) <= x)
		{
			if(i + layer(j) + 1 <= x)
			{
				total += 1;
				++i;
			}
			total += patty(j);
			i += layer(j);
		}
		else
		{
			++i;
			--j;
		}
	}
	printf("%lld\n", total);
}