#include "plants.h"
#include <bits/stdc++.h>
using namespace std;
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define rep(i, a, b) for(int i = (a); i < (b); i++)
#define sz(v) ((int)((v).size()))
template<typename T>
void chmax(T &x, const T &v) { if (x < v) x = v; }
template<typename T>
void chmin(T &x, const T &v) { if (x > v) x = v; }
using pii = pair<int, int>;
using vi = vector<int>;
string to_string(string s) { return s; }
template <typename T> string to_string(T v) {
bool first = true;
string res = "[";
for (const auto &x : v) {
if (!first)
res += ", ";
first = false;
res += to_string(x);
}
res += "]";
return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
void dbg_out() { cout << endl; }
template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) {
cout << ' ' << to_string(H);
dbg_out(T...);
}
#ifdef DEBUG
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif
const int INF = 1e9;
struct ArgMax {
inline pii op(pii a, pii b) { return max(a, b); }
const pii e {-INF, -1};
int N;
vector<pii> tree, lazy;
ArgMax(int __n) {
N = 1;
while (N < __n) N *= 2;
tree.assign(2*N, e);
lazy.assign(2*N, e);
}
void update(int i, int x) {
i += N;
tree[i] = {x, i-N};
while (i > 1) {
i /= 2;
tree[i] = op(tree[2*i], tree[2*i+1]);
}
}
pii _query(int L, int R) {
L += N, R += N+1;
pii res = e;
while (L < R) {
if (L & 1) res = op(res, tree[L++]);
if (R & 1) res = op(res, tree[--R]);
L /= 2, R /= 2;
}
return res;
}
int circMax(int L, int R) {
return (L > R ? max(_query(L, N-1), _query(0, R)) : _query(L, R)).second;
}
};
struct MinAdd {
inline int op(int a, int b) { return min(a, b); }
const int e = INF;
int N;
vector<int> tree, lazy;
void init(vector<int> v) {
N = 1;
while (N < (int)v.size()) N *= 2;
tree.assign(2*N, e);
lazy.assign(2*N, 0);
for (int i = 0; i < (int)v.size(); ++i) {
tree[N+i] = v[i];
}
for (int i = N-1; i >= 1; --i) {
tree[i] = op(tree[2*i], tree[2*i+1]);
}
}
void push(int node) {
tree[node] += lazy[node];
if (node < N) {
lazy[2*node] += lazy[node];
lazy[2*node+1] += lazy[node];
}
lazy[node] = 0;
}
void _add(int lq, int rq, int delta) {
auto F = [&] (auto f, int node, int lno, int rno) -> void {
push(node);
if (lq <= lno && rno <= rq) {
lazy[node] += delta;
push(node);
} else if (lno <= rq && lq <= rno) {
int mid = (lno+rno)/2;
f(f, 2*node, lno, mid);
f(f, 2*node+1, mid+1, rno);
tree[node] = op(tree[2*node], tree[2*node+1]);
}
};
F(F, 1, 0, N-1);
}
optional<int> _popZero(int lq, int rq) {
optional<int> ret = nullopt;
auto F = [&] (auto f, int node, int lno, int rno) {
push(node);
if (ret || tree[node] > 0 || rno < lq || rq < lno) {
return;
} else if (node >= N) {
tree[node] = e;
ret = node - N;
} else {
int mid = (lno+rno)/2;
f(f, 2*node, lno, mid);
f(f, 2*node+1, mid+1, rno);
tree[node] = op(tree[2*node], tree[2*node+1]);
}
};
F(F, 1, 0, N-1);
return ret;
}
optional<int> circleGet(int L, int R) {
if (L > R) {
auto a = _popZero(L, N-1);
return (a ? a : _popZero(0, R));
}
return _popZero(L, R);
}
void circleDecr(int L, int R) {
if (L > R) {
_add(L, N-1, -1);
_add(0, R, -1);
} else {
_add(L, R, -1);
}
}
};
MinAdd util;
int N, K;
int add(int x, int y) {
x += y;
if (x >= N) x -= N;
return x;
}
int sub(int x, int y) {
x -= y;
if (x < 0) x += N;
return x;
}
int anti(int x, int y) { return sub(y, x); }
vector<int> relative, height;
int insertHeight;
bool pop(int L, int R) {
optional<int> ret = util.circleGet(L, R);
if (!ret) return false;
for (; ret; ret = util.circleGet(L, R)) {
int cur = *ret;
pop(sub(cur,K-1), sub(cur, 1));
height[cur] = insertHeight--;
util.circleDecr(sub(cur,K-1), sub(cur,1));
}
return true;
}
const int LG = 18;
static_assert((1<<LG) >= 200'000);
vector<vi> lft, rgt;
void init(int _k, std::vector<int> _r) {
K = _k;
relative = _r;
N = _r.size();
//--
util.init(relative);
height.assign(N, -1);
insertHeight = N-1;
while(pop(0, N-1));
dbg(height);
//-
lft.assign(LG, vi(N, -1)), rgt.assign(LG, vi(N, -1));
ArgMax st(N);
vector<int> order(N);
iota(all(order), 0);
sort(all(order), [&] (int i, int j) { return height[i] < height[j]; });
for (int i : order) {
lft[0][i] = st.circMax(sub(i,K-1), sub(i,1));
rgt[0][i] = st.circMax(add(i,1), add(i,K-1));
st.update(i, height[i]);
}
function<int(int, int)> dist = sub;
auto jmp = &lft;
rep(_, 0, 2) {
rep(lvl, 0, LG-1) rep(node, 0, N) {
int mid = (*jmp)[lvl][node];
if (mid != -1) {
int nxt = (*jmp)[lvl][mid];
if (dist(node,mid)+dist(mid,nxt) < N) {
(*jmp)[lvl+1][node] = nxt;
}
}
}
jmp = &rgt, dist = anti;
}
dbg(lft[0]);
dbg(rgt[0]);
}
int cercle(int x, int y) { return min(sub(x,y),sub(y,x)); }
bool superieur(int depart, int dest, vector<vi> &jmp, int (*dist)(int, int)) {
int cur = depart;
int iniDist = dist(depart, dest);
dbg(depart, dest, iniDist);
for (int lvl = LG-1; lvl >= 0; --lvl) {
int prop = jmp[lvl][cur];
if (prop != -1) dbg(lvl, cur, prop);
if (prop != -1 && dist(depart,cur) + dist(cur,prop) < iniDist) {
cur = prop;
}
}
return cercle(cur,dest) < K && height[cur] > height[dest];
}
bool sup(int x, int y) {
return superieur(x, y, lft, sub) || superieur(x, y, rgt, anti);
}
int compare_plants(int x, int y) {
bool xy = sup(x,y), yx = sup(y,x);
return xy - yx;
}
