#include "cycle.h"
#include <bits/stdc++.h>
using namespace std;
mt19937 rng (chrono::steady_clock::now().time_since_epoch().count());
int random (int l, int r) {
return uniform_int_distribution <int> (l, r) (rng);
}
int sum, n;
int ask (int x) {
sum += x; sum %= n;
return jump(x);
}
void escape (int _N) {
n = _N;
assert(n != 2);
sum = 0;
if (ask(0)) {
//p >= ceil(n / 2)
//p + x < ceil(n / 2)
while (ask(random(n / 2, n - 1)));
int x = sum;
int l = 0, r = x, ans;
while (l <= r) {
int mid = (l + r) / 2;
if (!ask((mid - sum + n) % n)) {
r = mid - 1; ans = mid;
} else {
l = mid + 1;
}
}
ask((ans - sum + n - 1) % n);
} else {
//p < ceil(n / 2)
//p + x >= ceil(n / 2)
while (!ask(random(n / 2, n - 1)));
int x = sum;
int l = 0, r = x, ans;
while (l <= r) {
int mid = (l + r) / 2;
if (ask((mid - sum + n) % n)) {
r = mid - 1; ans = mid;
} else {
l = mid + 1;
}
}
ask((ans - sum + (n / 2) + n) % n);
}
}
