#include <bits/stdc++.h>
using namespace std;

using ll=int64_t;
#define int ll

#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define REP(i,b) FOR(i,0,b)
#define MP make_pair
#define PB push_back
#define ALL(x) x.begin(),x.end()
#ifdef MAROON_LOCAL
#define cerr (cerr<<"-- line "<<__LINE__<<" -- ")
#else
class CerrDummy{}cerrDummy;
template<class T>
CerrDummy& operator<<(CerrDummy&cd,const T&){
	return cd;
}
using charTDummy=char;
using traitsDummy=char_traits<charTDummy>;
CerrDummy& operator<<(CerrDummy&cd,basic_ostream<charTDummy,traitsDummy>&(basic_ostream<charTDummy,traitsDummy>&)){
	return cd;
}
#define cerr cerrDummy
#endif
#define REACH cerr<<"reached"<<endl
#define DMP(x) cerr<<#x<<":"<<x<<endl
#define ZERO(x) memset(x,0,sizeof(x))
#define ONE(x) memset(x,-1,sizeof(x))

using pi=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"{";
	REP(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"}";
	return os;
}

ll read(){
	ll i;
	scanf("%" SCNd64,&i);
	return i;
}

void printSpace(){
	printf(" ");
}

void printEoln(){
	printf("\n");
}

void print(ll x,int suc=1){
	printf("%" PRId64,x);
	if(suc==1)
		printEoln();
	if(suc==2)
		printSpace();
}

string readString(){
	static char buf[3341000];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341000];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(b<a)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

#define CAPITAL
void Yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void No(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

const int Nmax=21;
const int S=1<<Nmax;
int dp[Nmax][S],nx[S][2],cnt[S];
int idx(int len,int bit){
	return (1<<len)-1+bit;
}
void Init(int n){
	REP(i,n+1){
		REP(bit,1<<i){
			int w=idx(i,bit);
			REP(k,2){
				nx[w][k]=-1;
				for(int j=i-1;j>=0;j--)if(((bit>>j)&1)==k){
					nx[w][k]=j;
					break;
				}
			}
		}
	}
}

signed main(){
	int n=read(),atleast=read();
	Init(n);
	REP(i,n+1){
		string x=readString();
		REP(bit,1<<i)if(x[bit]=='1')
			dp[0][idx(i,bit)]=1;
	}
	REP(a,n+1){
		FOR(i,a,n+1){
			REP(bit,1<<i){
				int w=idx(i,bit);
				int len=i-a;
				int dec=bit>>len;
				int rem=(bit&((1<<len)-1));
				int u=idx(len,rem);
				REP(k,2)if(nx[u][k]!=-1){
					int p=dec;
					p<<=1;
					p+=k;
					p<<=nx[u][k];
					p+=(rem&((1<<nx[u][k])-1));
					dp[a+1][idx(a+1+nx[u][k],p)]+=dp[a][w];
				}
				cerr<<dec<<" "<<a<<" "<<w<<" "<<dp[a][w]<<endl;
				cnt[idx(a,dec)]+=dp[a][w];
			}
		}
	}
	for(int i=n;i>=0;i--){
		REP(bit,1<<i)if(cnt[idx(i,bit)]>=atleast){
			string ans(i,'?');
			REP(j,i)ans[i-1-j]=char('0'+((bit>>j)&1));
			cout<<ans<<endl;
			return 0;
		}
	}
	cout<<endl;
}


Measured memory_bytes: 391536