#include <bits/stdc++.h>
#include "plants.h"
using namespace std;
typedef long long ll;
struct segTree{
pair<int, int> tree[1600002];
int lazy[1600002];
void init(int i, int l, int r, int *A){
lazy[i] = 0;
if(l==r){
tree[i] = make_pair(A[l], l);
return;
}
int m = (l+r)>>1;
init(i*2, l, m, A);
init(i*2+1, m+1, r, A);
tree[i] = min(tree[i*2], tree[i*2+1]);
}
void propagate(int i, int l, int r){
tree[i].first += lazy[i];
if(l!=r){
lazy[i*2] += lazy[i];
lazy[i*2+1] += lazy[i];
}
lazy[i] = 0;
}
void add(int i, int l, int r, int s, int e, int val){
propagate(i, l, r);
if(r<s || e<l) return;
if(s<=l && r<=e){
lazy[i] += val;
propagate(i, l, r);
return;
}
int m = (l+r)>>1;
add(i*2, l, m, s, e, val);
add(i*2+1, m+1, r, s, e, val);
tree[i] = min(tree[i*2], tree[i*2+1]);
}
pair<int, int> findMin(int i, int l, int r, int s, int e){
propagate(i, l, r);
if(r<s || e<l) return make_pair(INT_MAX, INT_MAX);
if(s<=l && r<=e) return tree[i];
int m = (l+r)>>1;
return min(findMin(i*2, l, m, s, e), findMin(i*2+1, m+1, r, s, e));
}
} tree;
struct mineSeg{
struct Node {
ll lmax; int lidx;
ll rmax; int ridx;
ll ans; int ansl, ansr;
ll sum;
Node(){}
Node(ll x, int idx){
lmax = rmax = ans = sum = x;
lidx = ridx = ansl = ansr = idx;
}
Node merge(const Node &r)const{
Node ret = *this;
if(ret.lmax < sum + r.lmax){
ret.lmax = sum + r.lmax;
ret.lidx = r.lidx;
}
ret.rmax += r.sum;
if(ret.rmax < r.rmax){
ret.rmax = r.rmax;
ret.ridx = r.ridx;
}
if(ret.ans < r.ans) ret.ans = r.ans, ret.ansl = r.ansl, ret.ansr = r.ansr;
if(ret.ans < rmax + r.lmax){
ret.ans = rmax + r.lmax;
ret.ansl = ridx, ret.ansr = r.lidx;
}
ret.sum += r.sum;
return ret;
}
} tree[1600002];
void init(int i, int l, int r, int *A){
if(l==r){
tree[i] = Node(A[l] ? 1 : -1e9, l);
return;
}
int m = (l+r)>>1;
init(i*2, l, m, A);
init(i*2+1, m+1, r, A);
tree[i] = tree[i*2].merge(tree[i*2+1]);
}
void change(int i, int l, int r, int idx, int x){
if(l==r){
tree[i] = Node(x ? 1 : -1e9, l);
return;
}
int m = (l+r)>>1;
if(idx <= m) change(i*2, l, m, idx, x);
else change(i*2+1, m+1, r, idx, x);
tree[i] = tree[i*2].merge(tree[i*2+1]);
}
} mineTree;
struct checkSeg{
int tree[1600002];
void init(int i, int l, int r){
if(l==r){
tree[i] = 0;
return;
}
int m = (l+r)>>1;
init(i*2, l, m);
init(i*2+1, m+1, r);
tree[i] = max(tree[i*2], tree[i*2+1]);
}
void update(int i, int l, int r, int idx, int val){
if(l==r){
tree[i] = val;
return;
}
int m = (l+r)>>1;
if(idx <= m) update(i*2, l, m, idx, val);
else update(i*2+1, m+1, r, idx, val);
tree[i] = max(tree[i*2], tree[i*2+1]);
}
int query(int i, int l, int r, int s, int e){
if(r<s || e<l) return 0;
if(s<=l && r<=e) return tree[i];
int m = (l+r)>>1;
return max(query(i*2, l, m, s, e), query(i*2+1, m+1, r, s, e));
}
} chkseg;
int n, k;
int arr[400002];
int sum[400002];
int ans[400002];
int ord[400002];
int L[400002], R[400002];
int Lsp[400002][20], Rsp[400002][20];
int Lg[400002][20], Rg[400002][20];
void init(int _k, vector<int> r) {
n = (int)r.size();
k = _k;
for(int i=1; i<=n; i++) arr[i] = r[i-1];
for(int i=n+1; i<=n*2; i++) arr[i] = arr[i-n];
tree.init(1, 1, n*2, arr);
mineTree.init(1, 1, n*2, arr);
for(int turn=n; turn>=1; turn--){
auto tmp = mineTree.tree[1];
if(tmp.ans < k-1) exit(1);
int loc = tmp.ansr % n + 1;
ans[loc] = turn;
ord[turn] = loc;
/// 1에서 0이 되는 위치들을 검색
int lim = loc+n, leftmost = lim-k+1;
while(leftmost < lim){
pair<int, int> tmp2 = tree.findMin(1, 1, n*2, leftmost, lim-1);
if(tmp2.first > 1) break;
int x = tmp2.second;
mineTree.change(1, 1, n*2, (x-1)%n+1, 0);
mineTree.change(1, 1, n*2, (x-1)%n+1+n, 0);
leftmost = x+1;
}
mineTree.change(1, 1, n*2, loc, 1);
mineTree.change(1, 1, n*2, loc+n, 1);
/// tree 변경
tree.add(1, 1, n*2, loc, loc, 1000000000);
tree.add(1, 1, n*2, loc+n, loc+n, 1000000000);
if(loc >= k){
tree.add(1, 1, n*2, loc-k+1, loc, -1);
tree.add(1, 1, n*2, loc-k+1+n, loc+n, -1);
}
else{
tree.add(1, 1, n*2, 1, loc, -1);
tree.add(1, 1, n*2, loc-k+1+n, loc+n, -1);
tree.add(1, 1, n*2, 2*n-(k-loc)+1, n*2, -1);
}
}
chkseg.init(1, 1, n*2);
for(int turn=1; turn<=n; turn++){
int x = ord[turn];
L[turn] = chkseg.query(1, 1, n*2, x+n-(k-1), x+n);
R[turn] = chkseg.query(1, 1, n*2, x, x+(k-1));
chkseg.update(1, 1, n*2, x, turn);
chkseg.update(1, 1, n*2, x+n, turn);
}
for(int i=1; i<=n; i++){
Lsp[i][0] = L[i], Rsp[i][0] = R[i];
if(ord[i] < ord[L[i]]) Lg[i][0] = -1;
if(ord[i] > ord[R[i]]) Rg[i][0] = 1;
}
for(int d=1; d<20; d++){
for(int i=1; i<=n; i++){
Lsp[i][d] = Lsp[Lsp[i][d-1]][d-1];
Rsp[i][d] = Rsp[Rsp[i][d-1]][d-1];
Lg[i][d] = Lg[i][d-1] + Lg[Lsp[i][d-1]][d-1];
Rg[i][d] = Rg[i][d-1] + Rg[Rsp[i][d-1]][d-1];
}
}
}
int compare_plants(int x, int y) {
x++, y++;
int def = ans[x] > ans[y] ? 1 : -1;
if(ans[x] < ans[y]) swap(x, y);
int tmp = ans[x];
ll lLim=0, rLim=0;
for(int d=19; d>=0; d--){
if(Lsp[tmp][d] == 0 || Lsp[tmp][d] < ans[y]) continue;
lLim += Lg[tmp][d];
tmp = Lsp[tmp][d];
}
lLim += ord[tmp];
tmp = ans[x];
for(int d=19; d>=0; d--){
if(Rsp[tmp][d] == 0 || Rsp[tmp][d] < ans[y]) continue;
rLim += Rg[tmp][d];
tmp = Rsp[tmp][d];
}
rLim += ord[tmp];
ll l = lLim, r = rLim;
if((r-l) >= n) return def;
l = (n - (-l%n))%n;
if(!l) l=n;
r = (n - (-r%n))%n;
if(!r) r=n;
if(r<l) r+=n;
if(l<=y && y<=r) return def;
if(l<=y+n && y+n<=r) return def;
return 0;
}
