//
// ~oisín~ C++ Template
//
#include <bits/stdc++.h>
#define MX_N 5001
#define mp make_pair
#define mod7 1000000007
#define modpi 314159
#define PI 3.141592653589793238
#define pb push_back
#define FastIO ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define All(a) a.begin(),a.end()
#define fi first
#define se second
#define ll long long int
#define ull unsigned long long int
int kx[8] = {+2, +2, -2, -2, +1, +1, -1, -1};
int ky[8] = {+1, -1, +1, -1, +2, -2, +2, -2};
int d9x[9] = {+1, +1, +1, +0, +0, +0, -1, -1, -1};
int d9y[9] = {+1, +0, -1, +1, +0, -1, +1, +0, -1};
int dx4[4] = {+0, +0, +1, -1};
int dy4[4] = {+1, -1, +0, +0};
ll gcd(ull a, ull b){
return (a==0)?b:gcd(b%a,a);
}
ll lcm(ull a, ull b){
return a*(b/gcd(a,b));
}
const long long INF = 1e18;
using namespace std;
bool make_test(string p);
string n_zeroes(int n){
string res = "";
for(int i=0;i<n;++i){
res += '0';
}
return res;
}
int longest_zeroes(int n){
int lo = 0;
int hi = n;
while(lo < hi){
int mid = (lo+hi+1)/2;
if(make_test(n_zeroes(mid))){
lo = mid;
}else{
hi = mid-1;
}
}
return lo;
}
string analyse(int n, int t){
int M = longest_zeroes(n);
int doubt = 0;
string res = n_zeroes(M);
while(doubt <= M){
if(make_test(res+'1')){
doubt = 0;
res += '1';
}else{
++doubt;
res += '0';
}
}
int lo = 0;
int hi = doubt;
while(lo < hi){
int mid = (lo+hi)/2;
if(make_test(res.substr(0, (int)res.size()-mid))){
hi = mid;
}else{
lo = mid+1;
}
}
res = res.substr(0, (int)res.size()-lo);
while((int)res.size() < n){
if(make_test('1' + res)){
res = '1' + res;
}else{
res = '0' + res;
}
}
return res;
}
