#include "dna.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define mod 1000000007
#define h1 7897897897897897
#define h2 7897466719774591
#define b1 98762051
#define b2 98765431
#define inf 1000000000
#define pi 3.1415926535897932384626
#define LMAX 9223372036854775807
#define ll long long
#define fi first
#define se second
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vi vector<int>
#define vl vector<ll>
#define vp vector<pii>
#define SET(a, b) memset(a, b, sizeof(a));
#define all(x) (x).begin(), (x).end()
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define FORD(i, a, b) for (int i = (a); i >= (b); i--)
int init(int n, char c) {
int lo = 1, hi = n, ans = 0;
while (lo <= hi) {
int mid = (lo + hi) / 2;
string s = string(mid, c);
if (make_test(s)) {
ans = mid;
lo = mid + 1;
} else {
hi = mid - 1;
}
}
return ans;
}
int right(int n, char c, string str) {
int lo = 1, hi = n, ans = 0;
while (lo <= hi) {
int mid = (lo + hi) / 2;
string s = str + string(mid, c);
if (make_test(s)) {
ans = mid;
lo = mid + 1;
} else {
hi = mid - 1;
}
}
return ans;
}
int left(int n, char c, string str) {
int lo = 1, hi = n, ans = 0;
while (lo <= hi) {
int mid = (lo + hi) / 2;
string s = string(mid, c) + str;
if (make_test(s)) {
ans = mid;
lo = mid + 1;
} else {
hi = mid - 1;
}
}
return ans;
}
string analyse(int n, int t) {
int maxzero = init(n, '0');
int maxone = n - maxzero;
//cout << maxzero << ' ' << maxone << endl;
if (maxzero == 0) {
return string(n, '1');
}
if (maxone == 0) {
return string(n, '0');
}
string s = string(maxzero, '0');
int rem = n - maxzero;
char next = '1';
while (rem > 0) {
int cnt = (next == '0' ? right(min(rem, maxzero), next, s) : right(min(rem, maxone), next, s));
if (cnt == 0) break;
s += string(cnt, next);
if (next == '0') next = '1';
else next = '0';
rem -= cnt;
}
next = '1';
while (rem > 0) {
int cnt = (next == '0' ? left(min(rem, maxzero), next, s) : left(min(rem, maxone), next, s));
if (cnt == 0) break;
s = string(cnt, next) + s;
if (next == '0') next = '1';
else next = '0';
rem -= cnt;
}
return s;
}
