#include <bits/stdc++.h>
#include "prize.h"
using namespace std;
map<int, vector<int>> ans;
vector<int> query(int x)
{
if (ans.count(x)) return ans[x];
return ans[x] = ask(x);
}
int dc(int ini, int fim, int qMen, int qL, int qR)
{
//Cases in which i don't have to test
if (ini > fim || qL + qR == qMen) return -1;
if (fim - ini <= 1)
{
vector<int> aL = query(ini), aR = query(fim);
if (aL[0]+aL[1] == 0) return ini;
if (aR[0]+aR[1] == 0) return fim;
return -1;
}
if (query(ini) == query(fim)) return -1;
//all of them are expensive
if (fim - ini + 1 == qMen - (qL + qR))
{
for (int i = ini; i <= fim; i++)
{
vector<int> a = query(i);
if (a[0]+a[1] == 0) return i;
}
return -1;
}
//get middle expensive
int mL = (ini+fim)>>1, mR = (ini+fim)>>1;
vector<int> aL, aR;
while (mL >= ini)
{
aL = query(mL);
if (aL[0]+aL[1] == 0) return mL;
if (aL[0]+aL[1] < qMen) --mL;
else break;
}
while (mR <= fim)
{
aR = query(mR);
if (aR[0]+aR[1] == 0) return mR;
if (aR[0]+aR[1] < qMen) ++mR;
else break;
}
//then divide and conquer
int x = dc(mR, fim, qMen, aR[0], qR);
if (x == -1) return dc(ini, mL, qMen, qL, aL[1]);
return x;
}
int find_best(int n)
{
//here to find expensive quantity -> P(expensive) ~ 1/sqrt(N)
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
vector<int> ids;
for (int i = 0; i < 10; i++) ids.push_back(uniform_int_distribution<int>(0, n-1)(rng));
vector<vector<int>> possQ;
for (auto x : ids) possQ.push_back(query(x));
int qMen = 1;
for (auto &x : possQ) qMen = max(qMen, x[0]+x[1]);
return dc(0, n-1, qMen, 0, 0);
}
