#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
#define block_of_code if(true)
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(a, b);}
ll lcm(ll a, ll b){return a / gcd(a, b) * b;}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ll mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double cur = rngesus(0, MASK(60) - 1);
cur /= MASK(60) - 1;
return l + cur * (r - l);
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
#include "plants.h"
ostream& operator << (ostream& os, pair<int, int> x){
os << "(" << x.first << ", " << x.second << ")";
return os;
}
struct SegmentTree{
int n;
vector<pair<int, int>> a;
vector<int> lazy;
SegmentTree(int _n, vector<int> b){
n = _n;
a.resize(n * 4 + 4);
lazy.resize(n * 4 + 4);
build_tree(0, n-1, 1, b);
}
void build_tree(int l, int r, int id, vector<int> &b){
if (l == r) {
a[id] = make_pair(b[l], l);
return;
}
int mid = (l + r) >> 1;
build_tree(l, mid, id * 2, b);
build_tree(mid+1, r, id * 2 + 1, b);
a[id] = min(a[id * 2], a[id * 2 + 1]);
}
void apply(int id, int la){
a[id].first += la;
lazy[id] += la;
}
void down(int id){
apply(id * 2, lazy[id]); apply(id * 2 + 1, lazy[id]);
lazy[id] = 0;
}
void update(int u, int v, int w, int l, int r, int id){
if (u <= l && r <= v){
apply(id, w);
return;
}
if (lazy[id]) down(id);
int mid = (l + r) >> 1;
if (u <= mid) update(u, v, w, l, mid, id * 2);
if (v > mid) update(u, v, w, mid+1, r, id * 2 + 1);
a[id] = min(a[id * 2], a[id * 2 + 1]);
}
int normie(int x){
x %= n;
if (x < 0) x += n;
return x;
}
void update(int u, int v, int w){
u = normie(u);
v = normie(v);
if (u <= v)
update(u, v, w, 0, n-1, 1);
else{
update(u, n-1, w, 0, n-1, 1);
update(0, v, w, 0, n-1, 1);
}
}
pair<int, int> get_min(){
return a[1];
}
};
const int N = 2e5 + 69, LOG_N = 20;
const int INF = 1e9 + 69;
int n, k;
int order[N * 2];
int nxt1[LOG_N][N * 2], nxt2[LOG_N][N*2];
int normie(int x){
x %= n;
if (x < 0) x += n;
return x;
}
void add_point(set<int> &all_pos, set<int> &valid_pos, int i){
if (all_pos.empty()){
all_pos.insert(i);
valid_pos.insert(i);
return;
}
int l = -1, r = -1;
auto it = all_pos.upper_bound(i);
if (it != all_pos.end())
r = *it;
if (it != all_pos.begin()){
it--;
l = *it;
}
if (l == -1) l = *all_pos.rbegin();
if (r == -1) r = *all_pos.begin();
valid_pos.erase(r);
if (normie(r - i) >= k) valid_pos.insert(r);
if (normie(i - l) >= k) valid_pos.insert(i);
all_pos.insert(i);
}
void erase_point(set<int> &all_pos, set<int> &valid_pos, int i){
all_pos.erase(i);
valid_pos.erase(i);
if (all_pos.empty()) return;
int l = -1, r = -1;
auto it = all_pos.upper_bound(i);
if (it != all_pos.end())
r = *it;
if (it != all_pos.begin()){
it--;
l = *it;
}
if (l == -1) l = *all_pos.rbegin();
if (r == -1) r = *all_pos.begin();
valid_pos.erase(r);
if (normie(r - l) >= k || l == r) valid_pos.insert(r);
}
void init(int _k, vector<int> r){
n = r.size(), k = _k;
SegmentTree st(n, r);
set<int> all_pos;
set<int> valid_pos;
for(int it = 0; it < n; ++it){
while(true){
pair<int, int> cur = st.get_min();
if (cur.first) break;
int pos = cur.second;
st.update(pos, pos, INF);
add_point(all_pos, valid_pos, pos);
}
int pos = *valid_pos.begin();
order[pos] = order[pos + n] = n - it;
st.update(pos - k + 1, pos - 1, -1);
erase_point(all_pos, valid_pos, pos);
}
set<pair<int, int>> S; S.insert(make_pair(0, 2 * n));
nxt1[0][2*n] = 2*n;
for(int i = 2 * n - 1; i >= 0; --i){
if (i + k < 2 * n) S.erase(make_pair(order[i + k], i + k));
auto it = S.upper_bound(make_pair(order[i], -1));
if (it != S.begin()){
it--;
pair<int,int> cur = *it;
nxt1[0][i] = cur.second;
}
S.insert(make_pair(order[i], i));
}
S.clear();
S.insert(make_pair(0, -1));
nxt2[0][0] = 0;
for(int i = 0; i < 2 * n; ++i){
if (i - k >= 0) S.erase(make_pair(order[i - k], i - k));
auto it = S.upper_bound(make_pair(order[i], -1));
if (it != S.begin()){
it--;
pair<int,int> cur = *it;
nxt2[0][i + 1] = cur.second + 1;
}
S.insert(make_pair(order[i], i));
}
for(int j = 1; j < LOG_N; ++j)
for(int i = 0; i <= 2 * n; ++i){
nxt1[j][i] = nxt1[j-1][nxt1[j-1][i]];
nxt2[j][i] = nxt2[j-1][nxt2[j-1][i]];
}
}
bool check_more_than(int x, int y){
// check if (x) > (y)
// walk from x to y
if (y - x < k){
return 1;
}
else{
for(int j = LOG_N - 1; j >= 0; --j) {
int _x = nxt1[j][x];
if (y - _x >= k) x = _x;
}
x = nxt1[0][x];
if (x == y || (x < y && order[x] > order[y])) return 1;
}
return 0;
}
bool check_less_than(int x, int y){
// check if (x) < (y)
// walk from y to x
if (y - x < k){
return 1;
}
else{
for(int j = LOG_N - 1; j >= 0; --j) {
int _y = nxt2[j][y+1]-1;
if (_y - x >= k) y = _y;
}
y = nxt2[0][y+1]-1;
if (x == y || (x < y && order[x] < order[y])) return 1;
}
return 0;
}
int compare_plants(int x, int y){
if (order[x] > order[y]){ // either x is larger than y, or it is inconclusive
if (check_more_than(x, y) || check_less_than(y, x + n)) return 1;
}
else{ // either x is larger than y, or it is inconclusive
if (check_more_than(y, x + n) || check_less_than(x, y)) return -1;
}
return 0;
}
