#include <bits/stdc++.h>
#define fi first
#define se second
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = 1; i <= (n); ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define rng(a) a.begin(),a.end()
#define maxs(x,y) (x = max(x,y))
#define mins(x,y) (x = min(x,y))
#define limit(x,l,r) max(l,min(x,r))
#define lims(x,l,r) (x = max(l,min(x,r)))
#define isin(x,l,r) ((l) <= (x) && (x) < (r))
#define pb push_back
#define sz(x) (int)(x).size()
#define pcnt __builtin_popcountll
#define uni(x) x.erase(unique(rng(x)),x.end())
#define snuke srand((unsigned)clock()+(unsigned)time(NULL));
#define show(x) cout<<#x<<" = "<<x<<endl;
#define PQ(T) priority_queue<T,v(T),greater<T> >
#define bn(x) ((1<<x)-1)
#define dup(x,y) (((x)+(y)-1)/(y))
#define newline puts("")
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
typedef long long int ll;
typedef unsigned uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
inline int in() { int x; scanf("%d",&x); return x;}
template<typename T>inline istream& operator>>(istream&i,v(T)&v)
{rep(j,sz(v))i>>v[j];return i;}
template<typename T>string join(const v(T)&v)
{stringstream s;rep(i,sz(v))s<<' '<<v[i];return s.str().substr(1);}
template<typename T>inline ostream& operator<<(ostream&o,const v(T)&v)
{if(sz(v))o<<join(v);return o;}
template<typename T1,typename T2>inline istream& operator>>(istream&i,pair<T1,T2>&v)
{return i>>v.fi>>v.se;}
template<typename T1,typename T2>inline ostream& operator<<(ostream&o,const pair<T1,T2>&v)
{return o<<v.fi<<","<<v.se;}
template<typename T>inline ll suma(const v(T)& a) { ll res(0); for (auto&& x : a) res += x; return res;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#define dame { puts("-1"); return 0;}
#define yn {puts("YES");}else{puts("NO");}
const int MX = 200005;
string bins(int x, int n) {
  string res;
  rep(i,n) res += "01"[x&1], x >>= 1;
  reverse(rng(res));
  return res;
}

vvi d;

int main() {
  int n,K;
  scanf("%d%d",&n,&K);
  d = vvi(n+1);
  rep(i,n+1) {
    string s;
    cin>>s;
    int m = sz(s);
    d[i] = vi(m);
    rep(j,m) {
      if (s[j] == '1') {
        d[i][j] = 1;
      }
    }
  }

  // vvi sd = d;
  {
    for (int i = n; i >= 1; --i) {
      int m = 1<<i;
      rep(j,m) {
        d[i-1][j>>1] += d[i][j];
      }
    }
  }

  // drep(i,n+1) {
  //   int m = 1<<i;
  //   rep(j,m) {
  //     cerr<<i<<" "<<bins(j,i)<<": "<<d[i][j]<<endl;
  //   }
  // }

  rrep(e,n) {
    int msk = bn(e);
    for (int i = n; i > e; --i) {
      int m = 1<<i;
      rep(j,m) {
        int a = j>>e&1, b = j>>(e-1)&1;
        if (a == b) continue;
        int nj = (j>>(e+1)<<e) | (j&msk);
        d[i-1][nj] += d[i][j];
      }
    }

    // drep(i,n+1) {
    //   int m = 1<<i;
    //   rep(j,m) {
    //     cerr<<i<<" "<<bins(j,i)<<": "<<d[i][j]<<endl;
    //   }
    // }
  }

  drep(i,n+1) {
    int m = 1<<i;
    rep(j,m) {
      if (d[i][j] >= K) {
        cout<<bins(j,i)<<endl;
        return 0;
      }
    }
  }
  return 0;
}






















Measured memory_bytes: 9712