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<iostream>
#include<vector>
#include<algorithm>
using namespace std;

int n;
long long k;
long long ans = 0;
int cntr = 0;
std::vector<long long> v;
std::vector<long long> p;
long long saiki(int a){
  cout << "Hi." << endl;
  if(a == 0){
    cntr++;
    ans++;
    return 0;
  }
  if(cntr >= k) return 0;
  cntr++;
  if(cntr >= k) return 0;
  if(cntr + v[a-1] <= k){
    cntr += v[a-1];
    ans += p[a-1];
  }
  else {
    saiki(a-1);
    return 0;
  }
  if(cntr >= k) return 0;
  ans++;
  cntr++;
  if(cntr >= k) return 0;
  if(cntr + v[a-1] <= k){
    cntr += v[a-1];
    ans += p[a-1];
  }
  else{
    saiki(a-1);
    return 0;
  }
  if(cntr >= k) return 0;
  cntr++;
}

int main(){
  v.push_back(1);
  p.push_back(1);
  cin >> n >> k;
  for(int i = 1; i <= n; i++){
    p.push_back(p[i-1]*2+1);
    v.push_back(v[i-1]*2+3);
  }
  saiki(n);
  cout << ans << ' ' << v[49] << ' ' << p[49] << endl;
}