#include <vector>
#include <numeric>
#include <algorithm>
#include <random>
#include <cmath>
#include <set>
// Declare interactor
long long collisions(std::vector<long long> x);
namespace {
std::vector<long long> get_divisors(long long val, long long limit) {
std::vector<long long> divs;
for (long long i = 1; i * i <= val; ++i) {
if (val % i == 0) {
if (i > limit) divs.push_back(i);
if (val / i > limit && val / i != i) divs.push_back(val / i);
}
}
return divs;
}
bool check_n(long long n) {
if (n <= 0) return false;
std::vector<long long> q = {1, n + 1};
return collisions(q) > 0;
}
}
int hack() {
// --- Phase 1: Difference Set Construction ---
// We construct a set that covers all differences up to ~490,000 using only ~1400 elements.
// Set S = {1, 2, ..., B} U {B, 2B, 3B, ..., B*B}
const long long B = 700;
std::vector<long long> diff_set;
for (int i = 1; i <= B; ++i) diff_set.push_back(i);
for (int i = 1; i <= B; ++i) diff_set.push_back(i * B);
// Sort and remove duplicates to be safe
std::sort(diff_set.begin(), diff_set.end());
diff_set.erase(std::unique(diff_set.begin(), diff_set.end()), diff_set.end());
if (collisions(diff_set) > 0) {
// We know n is likely small (<= 490,000).
// Use binary search on the standard range {1...k} to find exact n.
// We can search up to B*B safely.
int low = 2, high = B * B + 100;
int ans = high;
// Standard Binary Search
while (low <= high) {
int mid = low + (high - low) / 2;
// Create query {1, 2, ..., mid}
std::vector<long long> q(mid);
std::iota(q.begin(), q.end(), 1);
if (collisions(q) > 0) {
ans = mid;
high = mid - 1;
} else {
low = mid + 1;
}
}
return ans - 1;
}
// --- Phase 2: Birthday Attack ---
// Since we cleared small n, we can use a moderate K.
// K = 28000.
// Initial query: 28k. Isolation: ~28k. Total ~56k.
// Total including Phase 1 < 60k.
// This allows multiple retries within the 110k budget or ensures high score.
int K = 28000;
std::mt19937_64 rng(1337);
std::uniform_int_distribution<long long> dist(1, 20000000000LL);
while (true) {
std::vector<long long> current_set;
current_set.reserve(K);
std::set<long long> distinct_check;
while (current_set.size() < K) {
long long val = dist(rng);
if (distinct_check.insert(val).second) {
current_set.push_back(val);
}
}
if (collisions(current_set) > 0) {
// Isolate
while (true) {
// Optimization: Brute force differences for small sets
if (current_set.size() <= 64) {
for (size_t i = 0; i < current_set.size(); ++i) {
for (size_t j = i + 1; j < current_set.size(); ++j) {
long long diff = std::abs(current_set[i] - current_set[j]);
// Only check divisors > B (since we ruled out smaller n in Phase 1)
// Actually, let's just check > 1 to be safe, cost is negligible here.
std::vector<long long> cands = get_divisors(diff, 1);
for (long long cand : cands) {
if (check_n(cand)) return (int)cand;
}
}
}
break; // Should not reach here if collision exists
}
int sz = current_set.size();
int mid = sz / 2;
std::vector<long long> left_part(current_set.begin(), current_set.begin() + mid);
std::vector<long long> right_part(current_set.begin() + mid, current_set.end());
if (collisions(left_part) > 0) {
current_set = left_part;
} else if (collisions(right_part) > 0) {
current_set = right_part;
} else {
std::shuffle(current_set.begin(), current_set.end(), rng);
}
}
}
}
return -1;
}
