#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstring>
#include <assert.h>
#include <sys/time.h>
#include <fstream>
#include <iomanip>

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)  FOR(i,0,n)
#define REP(i,n)  FOR(i,0,n)
#define each(i,c) for(auto i=(c).begin(); i!=(c).end(); ++i)
#define EACH(i,c) for(auto i=(c).begin(); i!=(c).end(); ++i)
#define exist(s,e) ((s).find(e)!=(s).end())

#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#define deb(x) cerr << #x << " = " << (x) << " , ";
#define debl cerr << " (L" << __LINE__ << ")"<< endl;
#define sz(s) (int)((s).size())


#define clr(a) memset((a),0,sizeof(a))
#define nclr(a) memset((a),-1,sizeof(a))
#define pb push_back
#define INRANGE(x,s,e) ((s)<=(x) && (x)<(e))
#define MP(x,y) make_pair((x),(y))

double pi=3.14159265358979323846;

using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;

template<typename T> std::ostream& operator<<(std::ostream& os, const vector<T>& z){
	os << "[ ";
	REP(i,z.size())os << z[i] << ", " ;
	return ( os << "]" << endl);
}

template<typename T> std::ostream& operator<<(std::ostream& os, const set<T>& z){
	os << "set( ";
	EACH(p,z)os << (*p) << ", " ;
	return ( os << ")" << endl);
}

template<typename T,typename U> std::ostream& operator<<(std::ostream& os, const map<T,U>& z){
	os << "{ ";
	EACH(p,z)os << (p->first) << ": " << (p->second) << ", " ;
	return ( os << "}" << endl);
}

template<typename T,typename U> std::ostream& operator<<(std::ostream& os, const pair<T,U>& z){
	return ( os << "(" << z.first << ", " << z.second << ",)" );
}

double get_time(){
	struct timeval tv;
	gettimeofday(&tv, NULL);
	return tv.tv_sec + tv.tv_usec*1e-6;
}

typedef unsigned int uint32_t;
struct RND{
	uint32_t x;
	uint32_t y;
	uint32_t z;
	uint32_t w;
	RND(){
		x=123456789;
		y=362436069;
		z=521288629;
		w=88675123;
	}
	void init(int seed){
		x=123456789;
		y=362436069;
		z=521288629;
		w=seed+100;
		REP(i,10)get();
	}
	uint32_t get(){
		uint32_t t;
		t=x^(x<<11);
		x=y;y=z;z=w;
		w=(w^(w>>19))^(t^(t>>8));
		return w;
	}
};
RND rnd;

ll double_to_ll(double d){
	if(d>0)return d+0.5;
	return d-0.5;
}

ll N,K;
int memo[1<<19][240];
int target[1<<20][22];


int rec(int b1, int l1, int b2, int l2){
	int b = (b2<<l1)+b1;
	int l = (l1+l2)*(l1+l2+1)/2 + l2;
	if(l1+l2>N)return 0;
	if(l1+l2==N){
		return target[b][l1+l2];
	}

	int &ret = memo[b][l];
	if(ret!=-1)return ret;
	ll ans = 0;
	if(l1==0 && target[b2][l2]){
		ans += 1;
	}
	if(l1==0){
		ans += rec(b1, l1,  2*b2, l2+1 );
		ans += rec(b1, l1, 2*b2+1,  l2+1 );
	}
	else if( (b1>>(l1-1))%2==0 ){
		ans += rec(b1, l1-1, 2*b2, l2+1);
		ans += rec(b1, l1, 2*b2+1, l2+1 );
	}
	else if((b1>>(l1-1))%2==1 ){
		ans += rec(b1 - (1<<(l1-1) ), l1-1,  2*b2+1, l2+1  );
		ans += rec(b1, l1, 2*b2, l2+1 ) ;
	}
	else{
		assert(false);
	}
	return ret = min(ans, K);
}

void _main(istream &inp){
	inp >> N >> K;
	rep(i,N+1){
		string s;
		inp >> s;
		assert(s.size()==(1<<i));
		rep(j, (1<<i) ){
			if(s[j]=='1'){
				target[j][i]=1;
			}
			else target[j][i] = 0;
		}
	}
	nclr(memo);


	for(int len=20; len>=0; len--){
		rep(b,1<<len){
			string s;
			rep(i,len){
				if((b>>i)%2==0)s.push_back('0');
				else s.push_back('1');
			}
			reverse(s.begin(), s.end());
//			int res = rec(b, len, 0, 0);
//			if(res!=0){
//				debug(s);
//				debug(res);
//			}
			if(rec(b, len, 0, 0)>=K){
				cout << s << endl;
				return;
			}
		}
	}


}

int main(){
	if(0){
		ifstream ifs("test.txt");
		_main(ifs);
	}
	else{
		_main(cin);
	}
	return 0;
}


Measured memory_bytes: 582080