#include<bits/stdc++.h>
#include "prize.h"
#define pb push_back
#define x first
#define y second
using namespace std;
typedef pair<int, int> ii;
const int maxn = 2e5 + 5;
vector<int> A[maxn];
vector<int> V;
int F = -1;
void check(int x) {
if(A[x][0] + A[x][1] == 0) F = x;
}
void find(int L, int R) {
int lo = L, hi = R - 1;
while(lo <= hi) {
int mid = (lo + hi) / 2;
if(A[mid].size() == 0) A[mid] = ask(mid);
check(mid);
if(F != -1) return;
if(A[mid][0] + A[mid][1] < A[hi + 1][0] + A[hi + 1][1]) {V.pb(mid);return;}
if(A[mid][1] == A[hi + 1][1]) hi = mid - 1;
else lo = mid + 1;
}
}
void solve(int lo, int hi, int R) {
if(lo >= hi) return;
if(R == 0) return;
if(R == 1) {find(lo, hi);return;}
int mid = (lo + hi) / 2;
int mid1 = mid;
while(1) {
if(A[mid1].size() == 0) A[mid1] = ask(mid1);
check(mid);
if(F != -1) return;
if(A[mid1][0] + A[mid1][1] < A[hi][0] + A[hi][1]) V.pb(mid1), mid1--;
else break;
if(mid1 < lo) break;
}
int R1, R2;
if(mid1 == -1) R2 = R - (mid - mid1);
else R2 = A[mid1][1] - A[hi][1] - (mid - mid1);
R1 = R - R2;
solve(lo, mid1, R1);
solve(mid + 1, hi, R2);
}
int find_best(int n) {
if(n <= 5000) {
for(int i = 0;i < n;i++) {
A[i] = ask(i);
if(A[i][0] + A[i][1] == 0) return i;
}
}
int pos = -1;
int s = 473;
for(int i = n - 1;i >= n - s;i--) {
A[i] = ask(i);
check(i);
if(F != -1) return F;
if(pos == -1 || A[i][0] + A[i][1] > A[pos][0] + A[pos][1])
pos = i;
}
for(int i = pos + 1;i < n;i++) V.pb(i);
solve(0, pos, A[pos][0]);
return F;
}
