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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

#define inf 1<<30
#define pqueue priority_queue
#define mp make_pair
#define pb push_back
#define fn fill_n
typedef long long llong;
typedef unsigned long long ullong;
typedef pair<int, int> P;

llong n, x;
llong many[51] = {}, paty[51] = {};

llong solve(llong eat, int level){
	if(eat <= 1) return 0;
	if(level < 0) return 0;
	if(eat == many[level]) return paty[level];

	llong ret = 0;

	if(eat <= many[level]/2){
		eat--;
	}else{
		eat -= many[level]/2+1;
		ret = paty[level-1]+1;
	}

	return ret + solve(eat, level-1);
}

int main(){
	many[0] = 1, paty[0] = 1;
	cin >> n >> x;
	for(int i = 1; i <= n; i++){
		many[i] = many[i-1]*2+3;
		paty[i] = paty[i-1]*2+1;
	}

	cout << solve(x, n) << endl;

	return 0;
}