#ifndef hwe
#include "gap.h"
#endif
#include <bits/stdc++.h>
using namespace std;
#define popcount(n) (__builtin_popcountll((n)))
#define clz(n) (__builtin_clzll((n)))
#define ctz(n) (__builtin_ctzll((n)))
#define lg(n) (63 - __builtin_clzll((n)))
#define BIT(n, i) (((n) >> (i)) & 1ll)
#define MASK(i) (1ll << (i))
#define FLIP(n, i) ((n) ^ (1ll << (i)))
#define ON(n, i) ((n) | MASK(i))
#define OFF(n, i) ((n) & ~MASK(i))
#define Int __int128
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long long, int> pli;
typedef pair<int, long long> pil;
typedef vector<pair<int, int>> vii;
typedef vector<pair<long long, long long>> vll;
typedef vector<pair<long long, int>> vli;
typedef vector<pair<int, long long>> vil;
template <class T1, class T2>
bool maximize(T1 &x, T2 y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <class T1, class T2>
bool minimize(T1 &x, T2 y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <class T>
void remove_duplicate(vector<T> &ve) {
sort (ve.begin(), ve.end());
ve.resize(unique(ve.begin(), ve.end()) - ve.begin());
}
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
template <class T> T random(T l, T r) {
return uniform_int_distribution<T>(l, r)(rng);
}
template <class T> T random(T r) {
return rng() % r;
}
const int N = 1e6 + 5;
const int MOD = 1e9 + 7;
const int inf = 1e9;
const ll INF = 1e18;
#ifdef hwe
void MinMax(ll s, ll t, ll *mn, ll *mx) {
cerr << s << ' ' << t << '\n';
cin >> *mn >> *mx;
}
#endif
namespace sub1 {
ll a[N];
ll findGap(int n) {
a[0] = -1, a[n + 1] = INF + 1;
for (int i = 1; i <= (n + 1) / 2; ++i) {
MinMax(a[i - 1] + 1, a[n - i + 2] - 1, &a[i], &a[n - i + 1]);
}
ll ans = -INF;
for (int i = 2; i <= n; ++i) maximize(ans, a[i] - a[i - 1]);
return ans;
}
}
namespace sub2 {
ll findGap(int n) {
ll mi, ma;
MinMax(0, INF, &mi, &ma);
ll L = ma - mi, lowerbound = (L + n - 1 + n - 2) / (n - 1), block_size = lowerbound - 1;
ll last_max = -1, ans = lowerbound - 1;
for (ll i = mi; i <= ma; i += lowerbound) {
ll mn, mx;
MinMax(i, min(i + lowerbound - 1, ma), &mn, &mx);
if (mn != -1) {
if (last_max != -1) maximize(ans, mn - last_max);
last_max = mx;
}
}
return ans;
}
}
ll findGap(int t, int n) {
if (t == 1) return sub1::findGap(n);
return sub2::findGap(n);
}
#ifdef hwe
signed main() {
findGap(2, 3);
cerr << '\n'; return 0;
}
#endif
