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.

Examples

Input

2 7


Output

4


Input

1 1


Output

0


Input

50 4321098765432109


Output

2160549382716056
import sys
from collections import deque
import copy
import math
def get_read_func(fileobject):
    if fileobject == None :
        return raw_input
    else:
        return fileobject.readline

def print_and_exit(X, eated_P):
    if X == 0:
        print eated_P
        exit()

table = {}

def get_burger_size(L):
    global table
    if L in table:
        return table[L]
    if L == 0:
        table[0] = (1L, 1L)
        return (1L, 1L)

    l_1_burger = get_burger_size(L - 1)
    table[L - 1] = l_1_burger
    return  (3L + 2L * l_1_burger[0], 1L + 2L * l_1_burger[1])

g_eated = 0
g_eated_P = 0

def calc_eated(X, L, eated_P):
    X -= 1
    print_and_exit(X, eated_P)

    (eated_f, eated_P_f) = get_burger_size(L - 1)
    if X < eated_f:
        calc_eated(X, L - 1, eated_P)
    X -= eated_f
    eated_P += eated_P_f
    print_and_exit(X, eated_P)

    eated_P += 1
    X -= 1
    print_and_exit(X, eated_P)

    (eated_f, eated_P_f) = get_burger_size(L - 1)
    if X < eated_f:
        calc_eated(X, L - 1, eated_P)
    X -= eated_f
    eated_P += eated_P_f
    print_and_exit(X, eated_P)

    X -= 1
    print_and_exit(X, eated_P)



def main():
    if len(sys.argv) > 1:
        f = open(sys.argv[1])
    else:
        f = None
    read_func = get_read_func(f);
    input_raw = read_func().strip().split()
    [N, X] = [long(input_raw[0]), long(input_raw[1])]
    calc_eated(X, N, 0)


if __name__ == '__main__':
    main()
