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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
var a = [1]; //層の総数
var p = [1]; //パテの数
function f(n, x) {
    if (n == 0) {
        return  (x <= 0) ? 0 : 1;
    } else if (x <= 1 + a[n - 1]) {
        return f(n - 1, x - 1);
    } else {
        return p[n - 1] + 1 + f(n - 1, x - 2 - a[n - 1]);
    }
}
function Main(input) {
    var l0 = input.split(" ");
    var N = l0[0] - 0;
    var X = l0[1] - 0;
    for (let n = 1; n <= N; n++) {
        a.push(a[n - 1] * 2 + 3);
        p.push(p[n - 1] * 2 + 1);
    }
    console.log(f(N, X));
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));