#include "bits/extc++.h"
using namespace std;
template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
cerr << t;
((cerr << " | " << u), ...);
cerr << endl;
}
#ifdef DEBUG
#define dbg(...) \
cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \
dbgh(__VA_ARGS__)
#else
#define dbg(...)
#define cerr \
if (false) \
cerr
#endif
#define endl "\n"
#define long int64_t
#define sz(x) int(std::size(x))
template <typename T>
ostream& operator<<(ostream& out, const vector<T>& arr) {
out << "[";
for (int i = 0; i < sz(arr); i++) {
if (i) {
out << ", ";
}
out << arr[i];
}
return out << "]";
}
template <typename T>
T reversed(T arr) {
reverse(begin(arr), end(arr));
return arr;
}
struct ST1 {
struct Node {
int mx, ind;
Node operator+(const Node& n) const {
if (mx > n.mx) {
return *this;
}
return n;
}
Node with_lazy(int x) const {
return {mx + x, ind};
}
};
int n;
vector<Node> v, arr;
vector<int> lazy;
ST1(const vector<Node>& arr) : n(sz(arr)), v(4 * n), arr(arr), lazy(4 * n) {
build(1, 0, n - 1);
}
void build(int o, int l, int r) {
if (l == r) {
v[o] = arr[l];
return;
}
int mid = (l + r) / 2, lc = o * 2, rc = lc + 1;
build(lc, l, mid);
build(rc, mid + 1, r);
v[o] = v[lc] + v[rc];
}
void update(int o, int l, int r, int ql, int qr, int x) {
if (ql <= l && r <= qr) {
v[o].mx += x;
lazy[o] += x;
return;
}
int mid = (l + r) / 2, lc = o * 2, rc = lc + 1;
if (ql <= mid) {
update(lc, l, mid, ql, qr, x);
}
if (mid < qr) {
update(rc, mid + 1, r, ql, qr, x);
}
v[o] = (v[lc] + v[rc]).with_lazy(lazy[o]);
}
void update(int l, int r, int x) {
update(1, 0, n - 1, l, r, x);
}
Node query_all() const {
return v[1];
}
};
struct DS2 {
int n, m;
set<int> v, good;
DS2(int n, int m) : n(n), m(m) {}
bool check(set<int>::iterator it) const {
if (it == v.begin()) {
if (sz(v) == 1) {
return true;
}
return *it + n - *v.rbegin() >= m;
}
int cur = *it, prv = *(--it);
return cur - prv >= m;
}
void check_update(set<int>::iterator it) {
if (it == v.end()) {
return;
}
if (check(it)) {
good.insert(*it);
} else {
good.erase(*it);
}
}
void insert(int x) {
auto [it, inserted] = v.insert(x);
assert(inserted);
check_update(it);
check_update(++it);
check_update(v.begin());
}
void erase(int x) {
bool erased = !!v.erase(x);
assert(erased);
good.erase(x);
check_update(v.lower_bound(x));
check_update(v.begin());
}
};
vector<int> solve_layers(int m, const vector<int>& arr) {
int n = sz(arr);
ST1 st_arr(({
vector<ST1::Node> v(n);
for (int i = 0; i < n; i++) {
v[i] = {arr[i], i};
}
v;
}));
int ans_it = 0, ans_cnt = 0;
vector<int> ans(n);
DS2 m_imp(n, m);
while (ans_cnt < n) {
while (true) {
auto it = st_arr.query_all();
if (it.mx == m - 1) {
m_imp.insert(it.ind);
st_arr.update(it.ind, it.ind, -1e9);
} else {
break;
}
}
vector<int> c_vals(begin(m_imp.good), end(m_imp.good));
for (auto& cur : c_vals) {
ans_cnt++;
ans[cur] = ans_it;
if (cur - m + 1 < 0) {
st_arr.update(0, cur, +1);
st_arr.update(cur - m + 1 + n, n - 1, +1);
} else {
st_arr.update(cur - m + 1, cur, +1);
}
m_imp.erase(cur);
}
ans_it++;
}
dbg(ans);
return ans;
}
struct QConn {
int n, logn, m;
vector<int> layers;
vector<vector<int>> lift;
QConn() {}
QConn(int m, const vector<int>& _layers)
: n(sz(_layers)),
logn(__lg(n) + 3),
m(m),
layers(_layers),
lift(logn + 1, vector<int>(2 * n)) {
auto tmp = layers;
layers.insert(layers.end(), begin(tmp), end(tmp));
map<int, int> q;
for (int i = 2 * n - 1; i >= 0; i--) {
if (i + m < 2 * n) {
q.erase(layers[i + m]);
}
assert(!q.count(layers[i]));
q[layers[i]] = i;
auto it = q.upper_bound(layers[i]);
if (it == q.end()) {
lift[0][i] = -1;
} else {
lift[0][i] = it->second;
}
}
for (int i = 1; i <= logn; i++) {
for (int j = 0; j < 2 * n; j++) {
if (lift[i - 1][j] == -1) {
lift[i][j] = -1;
} else {
lift[i][j] = lift[i - 1][lift[i - 1][j]];
}
}
}
}
bool query_lt(int u, int v) const {
if (layers[u] >= layers[v]) {
return false;
}
if (v < u) {
v += n;
}
for (int i = logn; i >= 0; i--) {
int nu = lift[i][u];
if (nu != -1 && layers[nu] <= layers[v]) {
u = nu;
}
}
return v <= u;
}
};
struct Solver {
int n, m;
vector<int> layers;
QConn q_f, q_r;
Solver() {}
Solver(int m, const vector<int>& arr)
: n(sz(arr)),
m(m),
layers(solve_layers(m, arr)),
q_f(m, layers),
q_r(m, reversed(layers)) {
dbg(layers);
}
bool query_lt(int u, int v) const {
return q_f.query_lt(u, v) || q_r.query_lt(n - u - 1, n - v - 1);
}
int query(int u, int v) const {
if (query_lt(u, v)) {
return -1;
} else if (query_lt(v, u)) {
return 1;
}
return 0;
}
} solver;
void init(int m, vector<int> arr) {
solver = Solver(m, arr);
}
int compare_plants(int u, int v) {
return solver.query(u, v);
}
