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 <iostream>
#include <iomanip>
#include <string>
#include <vector>
#include <algorithm>
#include <map>
#include <queue>
#include <stack>
#include <set>
#include <cstdint>
#include <cstdio>
#include <cstring>
#include <utility>
#include <queue>

using namespace std;
typedef long long signed int ll;

constexpr int inf = INT32_MAX / 2;
constexpr int mod = 1000000007;
constexpr int maxn = 100000;

ll layer(ll n) {
	if (n == 0) return 1;
	return layer(n - 1) * 2 + 3;
}

ll patty(ll n) {
	if (n == 0) return 1;
	return patty(n - 1) * 2 + 1;
}

ll solve(ll n, ll x) {
	if (x <= 1) return 0;
	else if (x < 1 + layer(n - 1)) return solve(n - 1, x - 1);
	else if (x == 1 + layer(n - 1)) return patty(n - 1);
	else if (x == 1 + layer(n - 1) + 1) return patty(n - 1) + 1;
	else if (x < 1 + layer(n - 1) + 1 + layer(n - 1)) return patty(n - 1) + 1 + solve(n - 1, x - (1 + layer(n - 1) + 1));
	else if (x == 1 + layer(n - 1) + 1 + layer(n - 1)) return patty(n - 1) + 1 + patty(n - 1);
	else if(x == 1 + layer(n-1)+1+layer(n-1)+1)return patty(n - 1) + 1 + patty(n - 1);
	else throw;
}

int main() {
	ll n, x;
	cin >> n >> x;
	cout << solve(n, x) << endl;
}