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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case, unused)]
use std::cmp::*;
use std::collections::*;
use std::f64::consts::*;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
pub trait BinarySearch<T> {
    fn lower_bound(&self, value: &T) -> usize;
    fn upper_bound(&self, value: &T) -> usize;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, value: &T) -> usize {
        let mut l = 0;
        let mut r = self.len();

        while l != r {
            let m = (l + r) / 2;
            match self[m].cmp(value) {
                Ordering::Less => {
                    l = m + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    r = m;
                }
            }
        }
        r
    }

    fn upper_bound(&self, value: &T) -> usize {
        let mut l = 0;
        let mut r = self.len();

        while l != r {
            let m = (l + r) / 2;
            match self[m].cmp(value) {
                Ordering::Equal | Ordering::Less => {
                    l = m + 1;
                }
                Ordering::Greater => {
                    r = m;
                }
            }
        }
        l
    }
}

fn f(n: usize, x: i64, b: Vec<i64>, p: Vec<i64>) -> i64 {
    if n == 0 {
        if x <= 0 {
            0
        } else {
            1
        }
    } else {
        if x <= 1 + b[n - 1] {
            f(n - 1, x - 1, b, p)
        } else {
            p[n - 1] + 1 + f(n - 1, x - (2 + b[n - 1]), b, p)
        }
    }
}

fn main() {
    input! {
        n: usize, x: i64,
    }
    let mut p = vec![0i64; n];
    let mut b = vec![0i64; n];
    p[0] = 1;
    b[0] = 1;
    for i in 1..n {
        p[i] = p[i - 1] * 2 + 1;
        b[i] = b[i - 1] * 2 + 3;
    }

    let ans = f(n, x, b, p);

    println!("{}", ans);
}