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 (1.42.0) (judge verdict: Accepted)

// -*- coding:utf-8-unix -*-

// use proconio::derive_readable;
use proconio::fastout;
use proconio::input;
// use std::convert::TryInto;
use libm::*;
use std::cmp::*;
use std::io::*;
use std::str::FromStr;
use superslice::*;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

//abc115-D
#[fastout]
fn main() {
    input![n: u64, x: u64];

    println!("{}", go(n, x));
}

fn go(level: u64, x: u64) -> u64 {
    // println!("{}", size_burger(50));
    // println!("{}, {}", level, x);

    let max_size = size_burger(level);

    if level == 0 && x == 1 {
        return 1;
    } else if x <= 1 {
        return 0;
    }

    if max_size - 1 <= x {
        return size_meet(level);
    }

    let bound = max_size / 2;
    if x <= bound {
        return go(level - 1, x - 1);
    } else {
        return size_meet(level - 1) + 1 + go(level - 1, x - size_burger(level - 1) - 2);
    }
}

fn size_burger(level: u64) -> u64 {
    (pow(2.0, level as f64 + 2.0) - 2.99999999999999999) as u64
}

fn size_meet(level: u64) -> u64 {
    (pow(2.0, level as f64 + 1.0) - 0.99999999999999999) as u64
}