//Author:xht37
#include <bits/stdc++.h>

#define ui unsigned int
#define ll long long
#define ul unsigned ll
#define ld long double

#define pi pair <int, int>
#define fi first
#define se second
#define mp make_pair

#define ls (p << 1)
#define rs (ls | 1)
#define md ((t[p].l + t[p].r) >> 1)

#define vi vector <int>
#define pb push_back
#define pq priority_queue

#define dbg(x) cerr << #x" = " << x << endl
#define debug(...) fprintf(stderr, __VA_ARGS__)

#define fl(x) freopen(x".in", "r", stdin), freopen(x".out", "w", stdout)

using namespace std;

namespace io {
	const int SI = 1 << 21 | 1;
	char IB[SI], *IS, *IT, OB[SI], *OS = OB, *OT = OS + SI - 1, c, ch[100];
	int f, t;
	#define gc() (IS == IT ? (IT = (IS = IB) + fread(IB, 1, SI, stdin), IS == IT ? EOF : *IS++) : *IS++)
	inline void flush() {
		fwrite(OB, 1, OS - OB, stdout), OS = OB;
	}
	inline void pc(char x) {
		*OS++ = x;
		if (OS == OT) flush();
	}

	template <class I>
	inline void rd(I &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c >= '0' && c <= '9'; x = (x << 3) + (x << 1) + (c & 15), c = gc());
		x *= f;
	}
	template <class I>
	inline void rd(I &x, I &y) {
		rd(x), rd(y);
	}
	template <class I>
	inline void rd(I &x, I &y, I &z) {
		rd(x), rd(y), rd(z);
	}
	template <class I>
	inline void rda(I *x, int n) {
		for (int i = 1; i <= n; i++) rd(x[i]);
	}
	inline void rdc(char &c) {
		for (c = gc(); c < 33 || c > 126; c = gc());
	}
	inline void rds(char *b, int &n) {
		for (c = gc(); c < 33 || c > 126; c = gc());
		for (n = 0; c >= 33 && c <= 126; b[++n] = c, c = gc());
		b[n+1] = '\0';
	}
	inline void rds(string &b) {
		for (c = gc(); c < 33 || c > 126; c = gc());
		for (b.clear(); c >= 33 && c <= 126; b.pb(c), c = gc());
	}

	template <class I>
	inline void print(I x, char k = '\n') {
		if (!x) pc('0');
		if (x < 0) pc('-'), x = -x;
		while (x) ch[++t] = x % 10 + '0', x /= 10;
		while (t) pc(ch[t--]);
		pc(k);
	}
	template <class I>
	inline void print(I x, I y) {
		print(x, ' '), print(y);
	}
	template <class I>
	inline void print(I x, I y, I z) {
		print(x, ' '), print(y, ' '), print(z);
	}
	template <class I>
	inline void printa(I *x, int n) {
		for (int i = 1; i <= n; i++) print(x[i], " \n"[i==n]);
	}
	inline void printc(char c) {
		pc(c);
	}
	inline void prints(char *b, int n) {
		for (int i = 1; i <= n; i++) pc(b[i]);
		pc('\n');
	}
	inline void prints(string b) {
		int n = b.length();
		while (t < n) pc(b[t++]);
		pc('\n'), t = 0;
	}
	struct Flush {
		~Flush() {
			flush();
		}
	} flusher;
}
using io::rd;
using io::rda;
using io::rdc;
using io::rds;
using io::print;
using io::printa;
using io::printc;
using io::prints;

const int N = 21;
int n, k, b[1<<N|1], t[1<<N|1][2], f[N][1<<N|1], ans = 1;
char c;

int main() {
	rd(n, k);
	for (int i = 0; i <= n; i++)
		for (int x = 0; x < 1 << i; x++)
			rdc(c), f[i][1<<i^x] = c - '0';
	b[0] = -1;
	for (int x = 1; x < 2 << n; x++) b[x] = b[x>>1] + 1;
	for (int x = 2; x < 2 << n; x++)
		if (x >> (b[x] - 1) & 1) t[x][1] = x ^ 1 << b[x], t[x][0] = t[t[x][1]][0];
		else t[x][0] = x ^ 3 << (b[x] - 1), t[x][1] = t[t[x][0]][1];
	for (int i = n; i; i--)
		for (int x = 1 << i; x < 2 << n; x++)
			if (f[i][x]) {
				int o = x >> i, B = (x & ((1 << i) - 1)) ^ 1 << i;
				if (t[B][0]) f[b[t[B][0]]][(o<<1^1)<<b[t[B][0]]^t[B][0]] += f[i][x];
				if (t[B][1]) f[b[t[B][1]]][(o<<1^0)<<b[t[B][1]]^t[B][1]] += f[i][x];
				f[0][o] += f[i][x];
			}
	for (int x = 2; x < 2 << n; x++)
		if (f[0][x] >= k && b[x] > b[ans]) ans = x;
	int i = n;
	while (!(ans >> i & 1)) i--;
	while (i--) printc((ans >> i & 1) + '0');
	return 0;
}

Measured memory_bytes: 194132