#include <bits/stdc++.h>
long long collisions(std::vector<long long> x);
int hack() {
int l = 5e8, r = 1e9;
while (l < r) {
int m = std::midpoint(l, r);
int b = std::sqrt(m - l + 1);
std::vector<long long> q;
for (int i = 1; i <= b; ++i) {
q.push_back(i);
}
for (int i = l + b; i <= m; i += b) {
q.push_back(i);
}
if (m + 1 > b) {
q.push_back(m + 1);
}
if (collisions(q)) {
r = m;
} else {
l = m + 1;
}
}
auto divisors = [](int x) {
std::vector<int> ans;
for (int i = 1; i * i <= x; ++i) {
if (x % i == 0) {
ans.push_back(i);
if (i * i != x) {
ans.push_back(x / i);
}
}
}
std::sort(ans.begin(), ans.end());
return ans;
};
for (auto &i : divisors(l)) {
if (collisions({1, i + 1})) {
return i;
}
}
return -1;
}
