#include <bits/stdc++.h>
// iostream is too mainstream
#include <cstdio>
// bitch please
#include <iostream>
#include <algorithm>
#include <cstdlib>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <list>
#include <cmath>
#include <iomanip>
#include <time.h>
#define dibs reserve
#define OVER9000 1234567890
#define ALL_THE(CAKE,LIE) for(auto LIE =CAKE.begin(); LIE != CAKE.end(); LIE++)
#define tisic 47
#define soclose 1e-8
#define chocolate win
// so much chocolate
#define patkan 9
#define ff first
#define ss second
#define abs(x) (((x) < 0)?-(x):(x))
#define uint unsigned int
#define dbl long double
#define pi 3.14159265358979323846
using namespace std;
// mylittledoge

using cat = long long;

#ifdef DONLINE_JUDGE
	// palindromic tree is better than splay tree!
	#define lld I64d
#endif

int main() {
	cin.sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(10);
	int N, K;
	cin >> N >> K;
	vector<string> S(N+1);
	for(int i = 0; i <= N; i++) cin >> S[i];
	vector< vector< vector<int> > > cnt(N+1);
	for(int i = 0; i <= N; i++) cnt[i].resize(1<<i, vector<int>(i+1, 0));
	for(int i = 0; i < (1<<N); i++) for(int j = 0; j <= N; j++) cnt[N][i][j] = S[N][i]-'0';
	for(int d = N-1; d >= 0; d--) {
		for(int i = 0; i < (1<<d); i++)
			cnt[d][i][d] = cnt[d+1][2*i][d+1] + cnt[d+1][2*i+1][d+1] + S[d][i]-'0';
		for(int i = 0; i < (1<<d); i++) for(int j = d-1; j >= 0; j--) {
			int l = i>>(d-j), r = i&((1<<(d-j))-1), c = (i>>(d-1-j))&1;
			cnt[d][i][j] = cnt[d+1][((2*l+1-c)<<(d-j))+r][j+1] + cnt[d][i][j+1];
		}
	}
	for(int d = N; d >= 0; d--) for(int i = 0; i < (1<<d); i++) if(cnt[d][i][0] >= K) {
		string ans;
		for(int j = d-1; j >= 0; j--) ans += '0'+((i>>j)&1);
		cout << ans << "\n";
		return 0;
	}
	return 0;
}

// look at my code
// my code is amazing
