#include "gap.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef pair<db,db> pd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
int pct(int x) { return __builtin_popcount(x); }
int bit(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
template<class A, class B> str ts(pair<A,B> p);
template<class A> str ts(complex<A> c) { return ts(mp(c.real(),c.imag())); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(char c) { str s = ""; s += c; return s; }
str ts(str s) { return s; }
str ts(const char* s) { return (str)s; }
str ts(vector<bool> v) {
bool fst = 1; str res = "{";
F0R(i,sz(v)) {
if (!fst) res += ", ";
fst = 0; res += ts(v[i]);
}
res += "}"; return res;
}
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
template<class T> str ts(T v) {
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
return "("+ts(p.f)+", "+ts(p.s)+")"; }
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << to_string(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 42
#endif
// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
/*vl dat = {3, 5, 6, 7, 8};
void MinMax(ll L, ll R, ll* a, ll* b){
bool works = 0;
for(int i = 0; i < sz(dat); i++){
if(L <= dat[i] && dat[i] <= R){
works = 1;
}
}
if(works == 0){
*a = -1;
*b = -1;
return;
}
for(int i = 0; i < sz(dat); i++){
if(dat[i] < L) continue;
*a = dat[i];
for(int j = i; j < sz(dat); j++){
if(dat[i] > R) break;
*b = dat[i];
}
break;
}
}*/
long long findGap(int T, int N)
{
if(T == 1){
ll L = 0;
ll R = ll(1E18)+5;
set<ll> nums;
for(int i = 0; i < (N+1)/2; i++){
ll a, b;
assert(L <= R);
MinMax(L, R, &a, &b);
if(a == -1){
break;
}
nums.insert(a);
nums.insert(b);
L = a+1;
R = b-1;
}
/*
while(L <= R){
ll a, b;
assert(L <= R);
MinMax(L, R, &a, &b);
//ps(L, R, a, b);
if(a == -1){
break;
}
nums.insert(a);
nums.insert(b);
if(a == b){
break;
}
L = a+1;
R = b-1;
if(L > R) break;
}*/
vl a;
ll ans = 0;
for(auto u: nums) a.pb(u);
//ps(nums);
//cout.flush();
assert(sz(nums) == N);
for(int i = 0; i < sz(a)-1; i++){
ans = max(ans, a[i+1]-a[i]);
}
return ans;
}
else{
ll L, R;
MinMax(0, ll(1E18), &L, &R);
ll step = (R-1-L)/(N-1);
ll rem = R-1-L-(step*(N-1));
if(R-L == N-1) return 1;
set<ll> nums;
nums.ins(L);
nums.ins(R);
ll curR = L;
for(ll i = 0; i < rem; i++){
ll curL = curR+1;
curR+=step+1;
ll a, b;
if(curL <= curR) MinMax(curL, curR, &a, &b);
if(a != -1){
nums.ins(a);
nums.ins(b);
}
}
for(ll i = rem; i < N-1; i++){
ll curL = curR+1;
curR+=step;
ll a, b;
if(curL <= curR) MinMax(curL, curR, &a, &b);
if(a != -1){
nums.ins(a);
nums.ins(b);
}
}
vl a;
ll ans = 0;
for(auto u: nums) a.pb(u);
//ps(nums);
//cout.flush();
for(int i = 0; i < sz(a)-1; i++){
ans = max(ans, a[i+1]-a[i]);
}
return ans;
}
}
/*
int main(){
ps(findGap(1, 5));
}*/
