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>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rep2(i, x, n) for (int i = x; i < (n); i++)
#define all(n) begin(n), end(n)
struct cww
{
    cww()
    {
        ios::sync_with_stdio(false);
        cin.tie(0);
    }
} star;
const long long INF = numeric_limits<long long>::max();
typedef long long ll;
typedef vector<int> vint;
typedef vector<char> vchar;
typedef vector<vector<int>> vvint;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef unsigned long long ull;
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
ull solve(ll x, int level, vll P, vll Len)
{
    if (x == 1)
    {
        return 0;
    }
    if (level == 1)
    {
        return min(3LL, x - 1);
    }
    if (x <= Len[level] / 2)
    {
        return solve(x - 1, level - 1, P, Len);
    }
    if (x == Len[level] / 2 + 1)
    {
        return P[level - 1] + 1;
    }
    else
    {
        return solve(x - Len[level - 1] - 2, level - 1, P, Len) + P[level - 1] + 1;
    }
}
int main()
{
    ll N, X;
    cin >> N >> X;
    vll P(N + 1), B(N + 1), Len(N + 1);
    P[0] = 1;
    Len[0] = 1;
    rep(i, N)
    {
        P[i + 1] = 2 * P[i] + 1;
        B[i + 1] = 2 * B[i] + 2;
        Len[i + 1] = P[i + 1] + B[i + 1];
    }
    ll x = X, level = N, ans = 0;

    cout << solve(X, N, P, Len);
    return 0;
}