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;

int main(){
  int64_t N, X;
  cin >> N >> X;
  //考察 (int j=1,2,3...i..3,2,1)
  //後ろから見ていくとBがi個、[Pが3個、Bがj個、Pが1個、Bがj個], Pが3個,Bがi個
  //string S = "P";
  //for(int i=0; i<N; i++){
    //S = "B" + S + "P" + S + "B";
    //cout << S << endl;
  //}
    
  int64_t ans = 0;
  int64_t cnt = N;
  bool end = false;
  for(int64_t i=1; i<N; i++){
    if(cnt + 3 < X){
      ans += 3;
      cnt += 3;
    }
    else{
      for(int j=0; j<3; j++){
        if(cnt >= X){
          end = true;
          break;
        }
        ans++;
        cnt++;
      }  
    }
    cnt += i;
    if(cnt >= X){
      end = true;
      break;
    }
    else{
      cnt++;
      ans++;
    }
    cnt += i;
  }
  
  for(int64_t i=N-1; i>=1; i--){
    if(end){
      break;
    }
    if(cnt + 3 < X){
      ans += 3;
      cnt += 3;
    }
    else{
      for(int j=0; j<3; j++){
        if(cnt >= X){
          end = true;
          break;
        }
        ans++;
        cnt++;
      }  
    }
    cnt += i;
    if(cnt >= X){
      end = true;
      break;
    }
    else{
      cnt++;
      ans++;
    }
    cnt += i;
  }
  
  for(int i=0; i<=3; i++){
    if(cnt >= X){
       end = true;
       break;
    }
    ans++;
    cnt++;
  }  
  cout << ans << endl;
}