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(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Read, StdoutLock, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_imports)]
use std::str::FromStr;

// christmas.rs --- Christmas
// author: Seong Yong-ju <sei40kr@gmail.com>

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

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

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

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

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

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

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

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
  ($($a:expr),*) => {
    println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
  }
}

#[allow(dead_code)]
fn with_bufwriter<F: FnOnce(BufWriter<StdoutLock>) -> ()>(f: F) {
    let out = stdout();
    let writer = BufWriter::new(out.lock());
    f(writer);
}

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

fn main() {
    input! {
      n: usize,
      x: i64
    }

    let mut a = vec![1i64; n + 1];
    let mut p = vec![1i64; n + 1];
    for i in 1..(n + 1) {
        a[i] = a[i - 1] * 2 + 3;
        p[i] = p[i - 1] * 2 + 1;
    }

    with_bufwriter(|mut out| writeln!(out, "{}", f(&a, &p, n, x)).unwrap());
}