// {{{ by shik
#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wunused-result"
#pragma GCC diagnostic ignored "-Wunused-function"
#define SZ(x) ((int)(x).size())
#define ALL(x) begin(x), end(x)
#define REP(i, n) for (int i = 0; i < int(n); i++)
#define REP1(i, a, b) for (int i = (a); i <= int(b); i++)
#define MP make_pair
#define PB push_back
using namespace std;
typedef int64_t LL;
typedef pair<int, int> PII;
typedef vector<int> VI;

namespace { namespace shik {

template<class T> void _R(T &x) { cin >> x; }
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%" SCNd64, &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template<class T, class... U> void R(T &head, U &... tail) { _R(head); R(tail...); }

template<class T> void _W(const T &x) { cout << x; }
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%" PRId64, x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template<class T> void _W(const vector<T> &x) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W(const T &head, const U &... tail) { _W(head); putchar(sizeof...(tail) ? ' ' : '\n'); W(tail...); }

#ifdef SHIK
#include "dump.hpp"
#else
#define dump(...)
#endif

template<class T, class F = less<T>> void sort_uniq(vector<T> &v, F f = F()) { sort(begin(v), end(v), f); v.resize(unique(begin(v), end(v)) - begin(v)); }
template<class T> inline T bit(T x, int i) { return (x >> i) & 1; }
template<class T> inline bool chkmax(T &a, const T &b) { return b > a ? a = b, true : false; }
template<class T> inline bool chkmin(T &a, const T &b) { return b < a ? a = b, true : false; }
template<class T> using MaxHeap = priority_queue<T>;
template<class T> using MinHeap = priority_queue<T, vector<T>, greater<T>>;

// }}}

const int N=21;

int tbl[1<<N];
void predo() {
    REP(i,1<<N) {
        int b=i&1;
        REP1(j,1,N-1) if ( ((i>>j)&1)==b ) {
            tbl[i]=j;
            break;
        }
    }
}

int n,m;
bitset<1<<N> has[N];
void input() {
    R(n,m);
    static char s[(1<<N)+1];
    REP1(i,0,n) {
        R(s);
        REP(j,1<<i) has[i][j]=s[j]-'0';
    }
}


VI dp[N][N];
void main() {
    predo();
    input();
    REP1(i,0,n) REP1(j,0,i) dp[i][j].resize(1<<i);
    REP1(i,0,n) REP(j,1<<i) dp[i][0][j]=has[i][j];
    for ( int i=n; i>=0; i-- ) {
        REP(j,i) {
            int msk=(1<<j)-1;
            REP(k,1<<i) {
                int me=dp[i][j][k];
                if ( !me ) continue;
                int l=k>>j;
                int r=k&msk;
                dp[i-1][j][((l>>1)<<j)|r]+=me;
                dp[i][j+1][k]+=me;
                int t=tbl[k>>j];
                if ( t>0 && t+j<i ) {
                    dp[i-t][j+1][((l>>t)<<j)|r]-=me;
                }
            }
        }
        REP(k,1<<i) if ( dp[i][i][k]>=m ) {
            string s;
            for ( int l=i-1; l>=0; l-- ) s.PB('0'+((k>>l)&1));
            W(s);
            return;
        }
    }
}

// {{{ main
}}
int main() { shik::main(); return 0; }
// }}}


Measured memory_bytes: 179200