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)

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

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 main() {
    let N: i64 = read();
    let X: i64 = read();
    let mut siz: Vec<i64> = vec![1];
    let mut n_p: Vec<i64> = vec![1];
    for i in 1..55 {
        let tmp = siz[i-1]*2+3;
        siz.push(tmp);
        let tmp = n_p[i-1]*2+1;
        n_p.push(tmp);
    }
    let mut depth = N as usize;
    let mut x = X-1;
    let mut ans: i64 = 0;
    loop{
        match x {
            _ if x <= 0 => {if depth==0 {ans += 1;} break;},
            _ if x < siz[depth]/2 => x -= 1,
            _ if x <= siz[depth]/2 => {ans += n_p[depth-1] + 1; break;},
            _ if x < siz[depth]-1 => {ans += n_p[depth-1] + 1; x -= siz[depth-1]+2},
            _ if x < siz[depth] => {ans += n_p[depth]; break;}
            _ => panic!()
        }
        depth -= 1;
    }
    println!("{}", ans);
}