#include "plants.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int mod(int a, int n) {
if ((a %= n) < 0) a += n;
return a;
}
int n;
int dist(int i, int j) {
return mod(j - i - 1, n) + 1;
}
struct MinTree {
int i, j;
int m, a = 0;
MinTree *l, *r;
MinTree(const vector<int>& v, int i, int j): i(i), j(j) {
if (j - i == 1) {
m = v[i];
l = r = nullptr;
} else {
int k = i + j >> 1;
l = new MinTree(v, i, k);
r = new MinTree(v, k, j);
m = min(l->m, r->m);
}
}
void visit() {
if (a) {
m += a;
if (l) l->a += a, r->a += a;
a = 0;
}
}
void inc(int I, int J, int A) {
if (I <= i && j <= J) {
a += A;
visit();
} else {
visit();
if (!(J <= i || j <= I)) {
l->inc(I, J, A);
r->inc(I, J, A);
m = min(l->m, r->m);
}
}
}
void get0s(int I, int J, vector<int>& t) {
visit();
if (m > 0 || J <= i || j <= I) return;
if (l) {
l->get0s(I, J, t);
r->get0s(I, J, t);
} else {
t.push_back(i);
}
}
void rinc(int I, int J, int A) {
while (I < j) {
I += j - i;
J += j - i;
}
while (i < I) {
I -= j - i;
J -= j - i;
inc(I, J, A);
}
}
void rget0s(int I, int J, vector<int>& t) {
while (I < j) {
I += j - i;
J += j - i;
}
while (i < I) {
I -= j - i;
J -= j - i;
get0s(I, J, t);
}
}
};
struct MaxTree {
int i, j;
pair<int,int> m;
MaxTree *l, *r;
MaxTree(int v, int i, int j): i(i), j(j), m(v, i) {
if (j - i == 1) {
l = r = nullptr;
} else {
int k = i + j >> 1;
l = new MaxTree(v, i, k);
r = new MaxTree(v, k, j);
}
}
void write(int I, int v) {
if (i <= I && I < j) {
if (l) {
l->write(I, v);
r->write(I, v);
m = std::max(l->m, r->m);
} else {
m = {v, i};
}
}
}
pair<int,int> max(int I, int J) {
if (I <= i && j <= J) {
return m;
} else if (J <= i || j <= I) {
return {-3, -3};
} else {
return std::max(l->max(I, J), r->max(I, J));
}
}
pair<int,int> rmax(int I, int J) {
while (I < j) {
I += j - i;
J += j - i;
}
pair<int,int> ans(-3, -3);
while (i < I) {
I -= j - i;
J -= j - i;
ans = std::max(ans, max(I, J));
}
return ans;
}
};
struct TreeTree {
int k;
vector<vector<int>> anc;
vector<ll> pard, dists;
vector<int> depth, height, down, upp, upi, lg;
vector<vector<int>> ups;
TreeTree() {}
TreeTree(const vector<int>& par, const vector<ll>& pard):
pard(pard), dists(par.size()), depth(par.size()), height(par.size()),
down(par.size(), -1), upp(par.size(), -1), upi(par.size(), -1), lg(par.size() + 1) {
int n = par.size();
for (k = 0; 1 << k <= n; k++);
anc = vector<vector<int>>(k, vector<int>(n, -1));
anc[0] = par;
for (int kk = 0; kk < k - 1; kk++) {
for (int i = 0; i < n; i++) {
int j = anc[kk][i];
anc[kk + 1][i] = anc[kk][j];
}
}
vector<vector<int>> adj(n);
vector<int> pre;
for (int i = 0; i < n; i++) {
if (par[i] == i) pre.push_back(i);
if (par[i] != i) adj[par[i]].push_back(i);
}
for (int f = 0; f < pre.size(); f++) {
int i = pre[f];
for (int j : adj[i]) {
depth[j] = depth[i] + 1;
dists[j] = dists[i] + pard[j];
pre.push_back(j);
}
}
reverse(pre.begin(), pre.end());
for (int i : pre) {
if (down[i] != -1)
height[i] = height[down[i]] + 1;
else
down[i] = i;
if (par[i] != i && (down[par[i]] == -1 || height[down[par[i]]] < height[i]))
down[par[i]] = i;
down[i] = down[down[i]];
}
reverse(pre.begin(), pre.end());
for (int s : pre) {
if (upi[s] == -1) {
int pi = ups.size();
ups.emplace_back(1, down[s]);
for (int it = 2*(height[s] + 1); it--;) {
ups.back().push_back(par[ups.back().back()]);
}
for (int idx = 0; idx < ups.back().size(); idx++) {
int i = ups.back()[idx];
if (upi[i] == -1) {
upi[i] = pi;
upp[i] = idx;
}
}
}
}
for (int i = 2; i < lg.size(); i++)
lg[i] = lg[i >> 1] + 1;
}
vector<pair<int,ll>> walk_up(int i, ll d, int t, int ct = 1) {
t = max(0, min(depth[i], t));
d -= dists[i];
if (t > 0) {
int kk = lg[t];
i = anc[kk][i];
// i = ups[upi[i]][upp[i] + t - (1 << kk)]; // should be wrong!
}
d += dists[i];
vector<pair<int,ll>> res;
for (; ct--; d -= pard[i], i = anc[0][i]) res.emplace_back(i, d);
return res;
}
};
vector<ll> depths;
void _jumpify(vector<int>& par, vector<ll>& dist, int k, int i) {
if (depths[i] == -1) {
if (par[i] == i) {
depths[i] = 0;
} else {
_jumpify(par, dist, k, par[i]);
depths[i] = dist[i] + depths[par[i]];
while (par[i] != par[par[i]] && i / k == par[i] / k) {
dist[i] += dist[par[i]];
par[i] = par[par[i]];
}
}
}
}
void jumpify(vector<int>& par, vector<ll>& dist, int k) {
depths = vector<ll>(par.size(), -1);
for (int i = 0; i < par.size(); i++) _jumpify(par, dist, k, i);
}
vector<int> vals;
TreeTree rttree, lftree;
int k;
void init(int k, vector<int> r) {
::k = k;
n = r.size();
vals = vector<int>(n);
MinTree curr(r, 0, n);
vector<int> likod(n), harap(n);
unordered_set<int> oks;
vector<int> cands;
for (int i = 0; i < n; i++) if (!r[i]) cands.push_back(i);
for (int x2 = 0, x1 = cands.size() - 1; x2 < cands.size(); x1 = x2++) {
int j1 = cands[x1], j2 = cands[x2];
harap[j1] = j2;
likod[j2] = j1;
if (dist(j1, j2) >= k) oks.insert(j2);
}
for (int v = n; v--;) {
int j = *oks.begin();
int j1 = likod[j], j2 = harap[j];
oks.erase(j);
vals[j] = v;
curr.inc(j, j + 1, n + 1);
curr.rinc(j - k + 1, j, -1);
vector<int> bagos;
curr.rget0s(j - k + 1, j, bagos);
if (v > 0) {
if (j == j1 && j == j2) {
j1 = bagos.back();
j2 = bagos.front();
}
bagos.insert(bagos.begin(), j1);
bagos.push_back(j2);
for (int x1 = 0, x2 = 1; x2 < bagos.size(); x1++, x2++) {
int j1 = bagos[x1], j2 = bagos[x2];
harap[j1] = j2;
likod[j2] = j1;
if (dist(j1, j2) >= k) {
oks.insert(j2);
} else if (oks.count(j2)) {
oks.erase(j2);
}
}
}
}
vector<int> lfs(n, -1), rts(n, -1);
MaxTree wals(-2, 0, n);
vector<int> inds(n);
for (int i = 0; i < n; i++) inds[vals[i]] = i;
for (int x : inds) {
wals.write(x, -1);
int m;
tie(m, lfs[x]) = wals.rmax(x - k + 1, x + 1);
tie(m, rts[x]) = wals.rmax(x, x + k);
wals.write(x, vals[x]);
}
vector<ll> lfdists(n), rtdists(n);
for (int i = 0; i < n; i++) {
lfdists[i] = dist(lfs[i], i);
rtdists[i] = dist(i, rts[i]);
}
jumpify(lfs, lfdists, k);
jumpify(rts, rtdists, k);
lftree = TreeTree(lfs, lfdists);
rttree = TreeTree(rts, rtdists);
}
bool is_fixed_right(int x, int y) {
for (auto [X, rem] : rttree.walk_up(x, dist(x, y), dist(x, y) / k - 1, 4)) {
if (abs(rem) < k && vals[X] >= vals[y]) return true;
}
return false;
}
bool is_fixed_left(int x, int y) {
for (auto [X, rem] : lftree.walk_up(x, dist(y, x), dist(y, x) / k - 1, 4)) {
if (abs(rem) < k && vals[X] >= vals[y]) return true;
}
return false;
}
int compare_plants(int x, int y) {
int mul = 1;
if (vals[x] < vals[y]) {
swap(x, y);
mul = -1;
}
return (is_fixed_right(x, y) || is_fixed_left(x, y)) * mul;
}
