#include "dna.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(abs(a), abs(b));}
ll lcm(ll a, ll b){return abs(a) / gcd(a, b) * abs(b);}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
// mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
string analyse(int n, int t){
int l = 0, r = n;
while(l < r){
int mid = (l + r + 1) >> 1;
if (make_test(string(mid, '0'))) l = mid;
else r = mid - 1;
}
if (l == 0) return string(n, '1');
string cur = string(l, '0');
int longest_zero_trail = l;
while(cur.size() < n){
string tmp = cur + "1";
if (make_test(tmp)){
cur = tmp;
longest_zero_trail = 0;
}
else{
cur.push_back('0');
longest_zero_trail++;
}
if (longest_zero_trail > l) break;
}
l = cur.size() - longest_zero_trail, r = cur.size();
while(l < r){
int mid = (l + r + 1) >> 1;
if (make_test(cur.substr(0, mid))) l = mid;
else r = mid - 1;
}
cur = cur.substr(0, l);
while(cur.size() < n){
if (make_test("1" + cur)) cur = "1" + cur;
else cur = "0" + cur;
}
return cur;
}
