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
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll num[54],n,k,cnt[54];
ll dfs(ll x,ll y){
	if (y>=num[x]-1) return cnt[x];
	if (x==0) return 1;
	ll res=0;
	ll go=min(y-1,num[x-1]);
	if (y>1) res+=dfs(x-1,go);
	if (y>num[x]/2) res++;
	go=min(y-num[x]/2-1,num[x-1]);
	if (y>num[x]/2+1) res+=dfs(x-1,go);
	return res;
}
int main(){
	num[0]=1;
	cnt[0]=1;
	for (ll i=1;i<=50;i++){
		num[i]=num[i-1]*2+3;
		cnt[i]=cnt[i-1]*2+1;
	}
	cin>>n>>k;
	cout<<dfs(n,k);
}