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: Time Limit Exceeded)

use std::io::*;
use std::str::FromStr;

//https://qiita.com/tubo28/items/e6076e9040da57368845
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")
}


fn make_burger(l:usize,burger:&mut Vec<char>,recipe:&mut Vec<Vec<char>>) -> Vec<char> {

    //println!("l:{} ",l);

    if !recipe[l].is_empty(){
        //println!("l:{} ",l);
        burger.extend(recipe[l].clone());
        return burger.to_vec();
    }

    if l == 0 {
        burger.push('P');
        recipe[l].push('P');
        return burger.to_vec();
    }else{
        burger.push('B');
        make_burger(l-1, burger, recipe);
        burger.push('P');
        make_burger(l-1, burger, recipe);
        burger.push('B');
    }

    recipe[l].extend(burger.clone());
    recipe[l].remove(0);
    //println!("no recipe l:{} ",l);
    burger.to_vec()
}

fn main(){
    let n:usize = read();
    let x:usize = read();
    let mut b = Vec::new();
    let mut recipe = vec![vec![];60];

    let burger:Vec<char> = make_burger(n,&mut b,&mut recipe);
   let ans = burger[0..x].iter().filter(|c| **c=='P').count();
    println!("{}",ans);
}