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 Python (2.7.6) (judge verdict: Accepted)

#!/usr/bin/env python
# -*- coding: utf-8 -*-

# AtCoder Beginner Contest 115：D - Christmas


# 各レベルの長さ
L = [1]+[0]*50
for i in range(50):
    L[i+1] = 3+L[i]*2
# print L

# 各レベルに含まれるパティの数
P = [1]+[0]*50
for i in range(50):
    P[i+1] = 1+P[i]*2
# print P


# 'B' + L[l-1] + 'P' + L[l-1] + 'B'
def lp(l, n):
    if l == 0:
        return 1
    elif n == 1:
        # 'B'
        return 0
    elif 1 < n <= 1+L[l-1]-1:
        # 'B' + L[l-1]の一つ手前まで
        return lp(l-1, n-1)
    elif n == 1+L[l-1]:
        # 'B' + L[l-1]
        return P[l-1]
    elif n == 1+L[l-1]+1:
        # 'B' + L[l-1] + 'P'
        return P[l-1]+1
    elif 1+L[l-1]+1 < n <= 1+L[l-1]+1+L[l-1]-1:
        # 'B' + L[l-1] + 'P' + L[l-1]の一つ手前まで
        return P[l-1] + 1 + lp(l-1, n-(1+L[l-1]+1))
    elif n == 1+L[l-1]+1+L[l-1]:
        # 'B' + L[l-1] + 'P' + L[l-1]
        return P[l-1] + 1 + P[l-1]
    elif n == 1+L[l-1]+1+L[l-1]+1:
        # 'B' + L[l-1] + 'P' + L[l-1] + 'B'
        return P[l-1] + 1 + P[l-1]
    else:
        print 'NG!'
        exit()


def main():
    N, X = [int(i) for i in raw_input().strip().split(' ')]

    print lp(N, X)


if __name__ == '__main__':
    main()