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 Go (1.14.1) (judge verdict: Accepted)

package main

import "fmt"

func solve(N int, X int, a []int, p []int) int {
	if N == 0 {
		if X <= 0 {
			return 0
		} else {
			return 1
		}
	} else if X <= 1+a[N-1] {
		return solve(N-1, X-1, a, p)
	} else {
		return p[N-1] + 1 + solve(N-1, X-2-a[N-1], a, p)
	}
}

func main() {
	// Code for D - Christmas
	var N, X int
	fmt.Scan(&N, &X)

	a := make([]int, N)
	p := make([]int, N)
	a[0] = 1
	p[0] = 1
	for i := 1; i < N; i++ {
		a[i] = 2*a[i-1] + 3
		p[i] = 2*p[i-1] + 1
	}

	fmt.Println(solve(N, X, a, p))
}