#include "plants.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
using str = string; // yay python!
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
#define tcT template<class T
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>;
tcT, size_t SZ> using AR = array<T,SZ>;
// pairs
#define mp make_pair
#define f first
#define s second
// vectors
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 1<<19;
const ll INF = 1e18; // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
// helper funcs
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down
tcT> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
#define tcTU tcT, class U
tcTU> T fstTrue(T lo, T hi, U f) {
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo+(hi-lo)/2;
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
lo --; assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo+(hi-lo+1)/2;
f(mid) ? lo = mid : hi = mid-1;
}
return lo;
}
tcT> void remDup(vector<T>& v) { // sort and remove duplicates
sort(all(v)); v.erase(unique(all(v)),end(v)); }
tcTU> void erase(T& t, const U& u) { // don't erase
auto it = t.find(u); assert(it != end(t));
t.erase(u); } // element that doesn't exist from (multi)set
// INPUT
#define tcTUU tcT, class ...U
tcT> void re(complex<T>& c);
tcTU> void re(pair<T,U>& p);
tcT> void re(vector<T>& v);
tcT, size_t SZ> void re(AR<T,SZ>& a);
tcT> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
tcTUU> void re(T& t, U&... u) { re(t); re(u...); }
tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; }
tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
tcT> void re(vector<T>& x) { trav(a,x) re(a); }
tcT, size_t SZ> void re(AR<T,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
return b ? "true" : "false";
#else
return ts((int)b);
#endif
}
tcT> str ts(complex<T> c) {
stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
tcTU> str ts(pair<T,U> p);
tcT> str ts(T v) { // containers with begin(), end()
#ifdef LOCAL
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
#else
bool fst = 1; str res = "";
for (const auto& x: v) {
if (!fst) res += " ";
fst = 0; res += ts(x);
}
return res;
#endif
}
tcTU> str ts(pair<T,U> p) {
#ifdef LOCAL
return "("+ts(p.f)+", "+ts(p.s)+")";
#else
return ts(p.f)+" "+ts(p.s);
#endif
}
// OUTPUT
tcT> void pr(T x) { cout << ts(x); }
tcTUU> void pr(const T& t, const U&... u) {
pr(t); pr(u...); }
void ps() { pr("\n"); } // print w/ spaces
tcTUU> void ps(const T& t, const U&... u) {
pr(t); if (sizeof...(u)) pr(" "); ps(u...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU> void DBG(const T& t, const U&... u) {
cerr << ts(t); if (sizeof...(u)) cerr << ", ";
DBG(u...); }
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
#define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
<< __FUNCTION__ << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif
// FILE I/O
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
/**
* Description: 1D range increment and sum query.
* Source: USACO Counting Haybales
* Verification: SPOJ Horrible
*/
template<class T, int SZ> struct LazySeg {
static_assert(pct(SZ) == 1); // SZ must be power of 2
const T ID = MOD; T comb(T a, T b) { return min(a,b); }
T seg[2*SZ], lazy[2*SZ];
LazySeg() { F0R(i,2*SZ) seg[i] = MOD, lazy[i] = 0; }
void push(int ind, int L, int R) { /// modify values for current node
seg[ind] += lazy[ind]; // dependent on operation
if (L != R) F0R(i,2) lazy[2*ind+i] += lazy[ind]; /// prop to children
lazy[ind] = 0;
} // recalc values for current node
void pull(int ind) { seg[ind] = comb(seg[2*ind],seg[2*ind+1]); }
void build() { ROF(i,1,SZ) pull(i); }
void upd(int lo,int hi,T inc,int ind=1,int L=0, int R=SZ-1) {
push(ind,L,R); if (hi < L || R < lo) return;
if (lo <= L && R <= hi) {
lazy[ind] = inc; push(ind,L,R); return; }
int M = (L+R)/2; upd(lo,hi,inc,2*ind,L,M);
upd(lo,hi,inc,2*ind+1,M+1,R); pull(ind);
}
T query(int lo, int hi, int ind=1, int L=0, int R=SZ-1) {
push(ind,L,R); if (lo > R || L > hi) return ID;
if (lo <= L && R <= hi) return seg[ind];
int M = (L+R)/2;
return comb(query(lo,hi,2*ind,L,M),query(lo,hi,2*ind+1,M+1,R));
}
int getMin(int ind=1, int L=0, int R=SZ-1) {
push(ind,L,R);
// dbg(ind,L,R,seg[ind]);
assert(seg[ind] == 0);
if (L == R) return L;
int M = (L+R)/2;
push(2*ind,L,M);
if (seg[2*ind] == 0) return getMin(2*ind,L,M);
return getMin(2*ind+1,M+1,R);
}
};
LazySeg<int,MX> L;
int n, k;
int jmp[2][20][MX];
vi val[2];
vi getHeights(vi r) {
trav(t,r) t = k-1-t;
F0R(i,n) L.seg[MX+i] = r[i];
L.build();
// dbg("BUILT");
assert(L.seg[1] == 0);
vi res; set<int> cand, ok; // OK as long
auto getPrev = [&](int x) { // x is in the set
auto it = cand.lb(x); assert(it != end(cand) && *it == x);
if (it == begin(cand)) it = end(cand);
return *prev(it);
};
auto getNex = [&](int x) { // x is not in the set
dbg("GETNEX",cand,x);
auto it = cand.lb(x);
assert(it == end(cand) || *it != x);
if (it == end(cand)) it = begin(cand);
if (it == end(cand)) return -1;
return *it;
};
auto tryIns = [&](int x) {
if (x == -1) return;
assert(cand.count(x));
if (ok.count(x)) ok.erase(x);
int y = getPrev(x);
if (y >= x) y -= n;
if (x-y >= k) ok.insert(x);
};
auto ins = [&](int x) {
dbg("INS");
L.upd(x,x,MOD);
int y = getNex(x); cand.insert(x);
tryIns(x), tryIns(y);
};
auto rem = [&](int l, int r) {
ckmax(l,0), ckmin(r,n-1);
if (l <= r) L.upd(l,r,-1);
};
auto del = [&](int x) {
// dbg("DEL");
assert(ok.count(x) && cand.count(x));
int l = x-k+1, r = x-1;
rem(l,r); rem(l+n,r+n);
ok.erase(x); cand.erase(x); res.pb(x);
int y = getNex(x); tryIns(y);
};
vi hei(n,-1);
F0R(_,n) {
// dbg("DOING",_);
assert(L.seg[1] >= 0);
while (L.seg[1] == 0) {
// dbg("WUT",L.seg[1],L.lazy[1]);
int x = L.getMin();
ins(x);
}
// dbg(ok);
assert(sz(ok));
int x = *begin(ok); del(x);
// dbg("REMOVING",x);
hei[x] = _;
}
trav(t,hei) assert(t != -1);
// dbg(hei);
return hei;
}
void initJump(int ind, vi h) {
h.insert(end(h),all(h));
val[ind] = h;
F0R(i,20) jmp[ind][i][sz(h)] = sz(h);
map<int,int> cur;
R0F(i,sz(h)) {
if (i+1 < sz(h)) cur[h[i+1]] = i+1;
if (i+k < sz(h)) cur.erase(h[i+k]);
auto it = cur.lb(h[i]);
if (it != end(cur)) jmp[ind][0][i] = it->s;
else jmp[ind][0][i] = sz(h);
FOR(j,1,20) jmp[ind][j][i] = jmp[ind][j-1][jmp[ind][j-1][i]];
}
}
void init(int _k, std::vector<int> r) {
k = _k; n = sz(r);
vi h = getHeights(r);
// dbg("OK",h);
initJump(0,h);
reverse(all(h));
initJump(1,h);
}
bool binjump(int ind, int l, int r) {
if (r < l) r += n;
// dbg("BINJUMP",ind,l,r,jmp[ind][0][l]);
R0F(i,20) if (jmp[ind][i][l] <= r)
l = jmp[ind][i][l];
return r-l < k && val[ind][l] <= val[ind][r];
}
bool inc(int x, int y) {
return binjump(0,x,y) || binjump(1,n-1-x,n-1-y);
}
int compare_plants(int x, int y) {
if (inc(x,y)) return -1;
if (inc(y,x)) return 1;
return 0;
}
