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>
#define ALL(a)  (a).begin(),(a).end()
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
typedef pair<long long, long long> Pll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<long long> vll;
typedef vector<vector<long long>> vvll;
template <typename T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template <typename T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const long long INF = 1LL << 60;
const int INT_INF = 1LL << 30;
#define MOD 1000000007LL

ll N, X;
vll length(51);
vll pnum(51);

ll func(ll lv, ll x){
  if(x == length.at(lv)) return pnum.at(lv);
  ll xx;
  if(x <= length.at(lv)/2){
    xx = x;
    if(xx == 1) return 0;
    return func(lv-1, xx-1);
  }
  else{
    xx = length.at(lv) - x;
    if(xx == 1) return pnum.at(lv);
    return pnum.at(lv) - func(lv-1, xx-1);
  }
}

int main(){
  cin >> N >> X;
  length.at(0) = 1LL;
  pnum.at(0) = 1LL;
  for(int i = 1; i <= N; i++){
    length.at(i) = 2LL * length.at(i-1) + 3LL;
    pnum.at(i) = 2LL * pnum.at(i-1) + 1LL;
  }
  cout << func(N, X) << endl;
}