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)

#![allow(non_snake_case)]
use proconio::input;
// use std::collections::HashMap;

// N次元バーガーを文字列で表す
// fn burger(level: u32) -> String {
//     if level == 0 {
//         return String::from("P");
//     }

//     let mut ans = String::from("B");
//     ans += &burger(level - 1);
//     ans += "P";
//     ans += &burger(level - 1);
//     ans += "B";

//     return ans;
// }

fn burger_size(level: usize) -> i64 {
    return 4 * 2_i64.pow(level as u32) - 3;
}


fn paty_size(level: usize) -> i64 {
    return 2 * 2_i64.pow(level as u32) - 1;
}

fn solve(N: usize, X: i64) -> i64 {
    // 食べてない
    if X == 0 {
        return 0;
    }

    // ベースケース
    if N == 0 && X == 1 {
        return 1;
    }

    if N == 0 && X > 1 {
        panic!("Someting wrong, N = 0, X = {}", X);
    }

    // N > 0 なので最下はパン
    if X == 1 {
        return 0;
    }

    let minus_1_all = burger_size(N - 1);
    let minus_1_p = paty_size(N - 1);

    // (level - 1) の途中で止まる
    if 1 < X && X < minus_1_all + 1 {
        // 最下のBだけ食べた
        return solve(N - 1, X - 1);
    }

    // ぴったりlevel-1
    if X == minus_1_all + 1 {
        return minus_1_p;
    }

    // level-1 + P
    if X == minus_1_all + 1 + 1 {
        return minus_1_p + 1;
    }

    // 2個目の(level - 1)の途中で止まる
    if X < 2 * minus_1_all + 2 {
        // 最下のBと1個目の(level-1)とPを食べた
        return minus_1_p + 1 + solve(N - 1, X - minus_1_all - 2);
    }

    return minus_1_p * 2 + 1;
}

fn main() {
    input! {
        N: usize,
        X: i64,
    }

    let ans = solve(N, X);
    println!("{}", ans);
}