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 Julia (0.5.0) (judge verdict: Wrong Answer)


parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)


#=function get_rank(N,X,D)
depth = 0
for j in 1:N
    depth += D[j]
    if depth > X
        return j,depth - X
    end
end 
end

function get_petty(rank,amari)
    ans = 0
    ans += 2^rank

end

function main()
    N,X = parseMap(split(readline()))
    D = []
    for i in N
        push!(D,2^(i+2)-3)
    end
    if X < D[N]/2
        rank,amari = get_rank(N,X,D)
        ans = get_petty(rank,amari)
    end
end    =#





N,X = parseMap(split(readline()))
D = []
P = []
for i in 0:N
    push!(D,2^(i+2)-3)
    push!(P,2^(i+1)-1)
end
#println(D,P)
function get_patty(N,X)
    if N == 0
    	#println("N==0")
        return 1
    elseif N == 1
    	#println("N==1")
        return 3   
    elseif X <= D[N-1] + 1
    	#println("under half")
        return get_patty(N - 1, X - 1)
    else 
    	#println("over half")
        amari = X - (1 + D[N - 1]) - 1 
        return get_patty(N - 1,amari) + P[N-1]
    end
end

ans = get_patty(N,X)
println(ans)