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distinctivecharacter.cpp
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// Michael Pfeifer
// Version 04, 2018/02/17
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef unsigned int uint;
typedef unsigned long long ull;
const ld pi = 4.0*atanl(1.0);
const int iinf = 1e9 + 10;
const ll inf = 1e18 + 10;
const int mod = 1000000007;
const ld prec = .000001;
#define enld endl
#define endl '\n'
#define pb push_back
#define debug(x) cout<<#x<<" -> "<<x<<'\n'
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define uni(x) (x).erase(unique(all(x)), (x).end())
#define rep(i, n) for (ll i = 0; i < (ll)(n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (ll)(n); ++i)
#define umap unordered_map
#define uset unordered_set
template<class TIn>
using indexed_set = tree<
TIn, null_type, less<TIn>,
rb_tree_tag, tree_order_statistics_node_update>;
void fast() {
ios::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
}
void file() {
auto a = freopen("a.in", "r", stdin);
auto b = freopen("a.out", "w", stdout);
if(!a || !b) cout << "uh oh" << endl;
}
int n, m;
int toint(string s) {
int ret = 0;
for(int i = 0; i < s.size(); i++) {
ret <<= 1;
if(s[i] == '1') {
ret++;
}
}
return ret;
}
string tobin(int n) {
string s;
while(n > 0) {
s.pb(n%2 + '0');
n /= 2;
}
while(s.length() < m) {
s.pb('0');
}
reverse(all(s));
return s;
}
int main() {
//file();
//fast();
cin >> n >> m;
int big = (1 << m);
vector<vector<int>> adj(big);
int curr = big;
while(curr--) {
for(int i = 1; i < big; i <<= 1) {
adj[curr].pb(curr ^ i);
}
}
vector<int> dist(big, iinf);
queue<int> q;
for(int i = 0; i < n; i++) {
string s;
cin >> s;
int t = toint(s);
dist[t] = 0;
q.push(t);
}
// BFS
while(!q.empty()) {
int here = q.front();
q.pop();
for(auto next : adj[here]) {
if(dist[next] == iinf) {
dist[next] = dist[here] + 1;
q.push(next);
}
}
}
int bestdist = 0;
int bestval = 0;
for(int i = 0; i < big; i++) {
if(dist[i] > bestdist) {
bestdist = dist[i];
bestval = i;
}
}
cout << tobin(bestval) << endl;
return 0;
}