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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.lang.reflect.Array;
import java.util.*;

public class Main {


    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        long x = sc.nextLong();
        System.out.println(f(n,x));
    }
    public static long a(long i){return ((long)(Math.pow(2,i+2)))-3;}
    public static long p(long i){return ((long)(Math.pow(2,i+1)))-1;}
    public static long f(long n, long x){
        if (x==1)return 0;
        else if (x<=a(n-1)+1)return f(n-1,x-1);
        else if (x==2+a(n-1))return p(n-1)+1;
        else if (x<=2+2*a(n-1))return p(n-1)+1+f(n-1,x-2-a(n-1));
        else return 2*p(n-1)+1;
    }
    public static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            }else{
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }else if(b == -1 || !isPrintableChar(b)){
                    return minus ? -n : n;
                }else{
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }
        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
    }
    public static class BasicMath {
        private final int MAX = 510000;
        private final int MOD = 1000000007;
        private final long[] fac = new long[MAX];
        private final long[] finv= new long[MAX];
        private final long[] inv = new long[MAX];
        public long factorial(long num){
            if (num<2)return 1;
            else return num*factorial(num-1);
        }
        public int arraySum(int[] array){
            int ans = 0;
            for (int value : array) ans += value;
            return ans;
        }
        public double log(double base,double antilogarithm){
            return Math.log(antilogarithm)/Math.log(base);
        }
        public int gcd(int x,int y){
            if (y==0)return x;
            else return gcd(y,x%y);
        }
        public int lcm(int x,int y){
            return x/gcd(x,y)*y;
        }
        public HashMap<Long,Long> factorization(long num){
            HashMap<Long,Long> hash = new HashMap<>();
            long n = num;
            long count = 2;
            while (n>1){
                while (n%count==0){
                    n/=count;
                    if (hash.containsKey(count))hash.put(count,hash.get(count)+1);
                    else hash.put(count,1L);
                }
                count++;
            }
            return hash;
        }
        public int sum(int[] num){
            int ans = 0;
            for (int i = 0; i < num.length;i++){
                ans += num[i];
            }
            return ans;
        }
        public int[] reduce(int small, int big){
            int ins = 2;
            while (ins<=small){
                if (small%ins==0&&big%ins==0){
                    small/=ins;
                    big/=ins;
                    ins = 2;
                }else {
                    ins++;
                }
            }
            return new int[]{small, big};
        }
        public int reduceCount(int small, int big){
            int ins = 2;
            int ans = 0;
            while (ins<=small){
                if (small%ins==0&&big%ins==0){
                    small/=ins;
                    big/=ins;
                    ins = 2;
                    ans++;
                }else {
                    ins++;
                }
            }
            return ans;
        }
        public int binarySearch(int[] array, int target){
            int pos = -1;
            int left = 0;
            int right = array.length-1;
            int middle;
            while (pos==-1&&left<=right){
                middle = (left+right)/2;
                if (array[middle]==target)pos=middle;
                else if (array[middle]>target)right=middle-1;
                else left=middle+1;
            }
            return pos;
        }
        public long modPow(long a, long n, long mod){
            long res = 1;
            while (n>0){
                if ((n&1)!=0)res = res*a%mod;
                a=a*a%mod;
                n >>= 1;
            }
            return res;
        }
        public long modinv(long a, long mod){return modPow(a,mod-2,mod);}
        public void COMinit(){
            fac[0]=1;
            fac[1]=1;
            finv[0]=1;
            finv[1]=1;
            inv[1]=1;
            for (int i=2;i<MAX;i++){
                fac[i]=fac[i-1]*i%MOD;
                inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
                finv[i]=finv[i-1]*inv[i]%MOD;
            }
        }
        public long COM(int n, int k){
            if (n<k)return 0;
            if (n<0||k<0)return 0;
            return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
        }
        public long HCOM(int n, int k){
            return COM(n+k-1,k);
        }
    }
    public static class Queue<T>{
        private final int max = 1000000;
        private final T[] queue = (T[]) new Object[max];
        private int tail = 0; private int head = 0;
        public void init(){this.head = 0; tail = 0;}
        public boolean isEmpty(){return (head==tail);}
        public boolean isFull(){return (head == (tail+1)%max);}
        public void enqueue(T v){
            if (isFull()){
                System.out.println("error: queue is full.");
                return;
            }
            queue[tail++] = v;
            if (tail == max) tail = 0;
        }
        public T dequeue(){
            if (isEmpty()){
                System.out.println("error: queue is empty");
                return null;
            }
            T res = queue[head];
            ++head;
            if (head == max) head = 0;
            return res;
        }
    }
    public static class Stack<T>{
        private final int max = 100000;
        private final T[] stack =(T[]) new Object[max];
        private int top = 0;
        public boolean isEmpty(){return (top==0);}
        public boolean isFull(){return (top==max);}
        public void init(){top=0;}
        public void push(T v){
            if (isFull()){
                System.out.println("error: stack is full.");
                return;
            }
            stack[top++] = v;
        }
        public T pop(){
            if (isEmpty()){
                System.out.println("error: stack is empty");
                return null;
            }
            return stack[--top];
        }
    }
    public static class Pair<T>{
        private T A;
        private T B;
        Pair(T a,T b){
            A=a;
            B=b;
        }
        public void changeA(T a){A=a;}
        public void changeB(T b){B=b;}
        public void changeAB(T a,T b){A=a;B=b;}
        public static Comparator numberSortWithA = new Comparator() {
            @Override
            public int compare(Object o1, Object o2) {
                Pair p = (Pair)o1;
                Pair q = (Pair)o2;
                if ((Long)p.A<(Long)q.A)return -1;
                else if ((long)p.A==(long)q.A)return 0;
                else return 1;
            }
        };
        public static Comparator numberSortWithB = new Comparator() {
            @Override
            public int compare(Object o1, Object o2) {
                Pair p = (Pair)o1;
                Pair q = (Pair)o2;
                if ((long)p.B<(long)q.B)return -1;
                else if ((long)p.B==(long)q.B)return 0;
                else return 1;
            }
        };
    }
    public static class Graph<T>{
        private final HashMap<T,HashSet<T>> graph = (HashMap<T,HashSet<T>>) new Object();
        private T[] nodeList;
        private HashMap<T,Integer> dictionary = new HashMap<>();
        private int Size;
        private int[] Depth;
        Graph(T[] nodes){
            for (T t : nodes)graph.put(t,new HashSet<>());
            Size = nodes.length;
            nodeList = nodes.clone();
            for (int i=0;i<Size;i++)dictionary.put(nodeList[i],i);
        }
        public void addEdge(T node1,T node2){
            if (graph.containsKey(node1)&&graph.containsKey(node2)){
                graph.get(node1).add(node2);
                graph.get(node2).add(node1);
            }
        }
        public int[] Depth(T root){
            Queue<T> q = new Queue<>();
            q.enqueue(root);
            boolean[] seen = new boolean[Size];
            Arrays.fill(seen, false);
            seen[dictionary.get(root)]=true;
            int[] depth = new int[Size];
            depth[dictionary.get(root)]=0;
            while (!q.isEmpty()){
                T v = q.dequeue();
                int vNum = dictionary.get(v);
                for (T u : graph.get(v)){
                    if (!seen[dictionary.get(u)]){
                        int uNum = dictionary.get(u);
                        seen[uNum]=true;
                        q.enqueue(u);
                        depth[uNum]=depth[vNum]+1;
                    }
                }
            }
            Depth = depth.clone();
            return depth;
        }
    }
}