#include "obstacles.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define MOD 998244353
#define MOD2 1000000007
#define vt vector
template <class T> using vvt = vt<vt<T>>;
template <class T> using vvvt = vt<vvt<T>>;
template <class T> using vvvvt = vt<vvvt<T>>;
typedef vt<int> vi;
typedef vvt<int> vvi;
typedef vvvt<int> vvvi;
typedef vvvvt<int> vvvvi;
typedef vt<ll> vl;
typedef vvt<ll> vvl;
typedef vvvt<ll> vvvl;
typedef vvvvt<ll> vvvvl;
#define endl '\n'
#define pb push_back
#define pf push_front
#define all(x) x.begin(),x.end()
#define sz(x) (int)((x).size())
#define mset multiset
#define fi first
#define se second
#define rep(i,a,b) for(int i=a;i<b;i++)
#define repl(i,a,b) for(ll i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define rrepl(i,a,b) for(ll i=a;i>=b;i--)
#define each(i,a) for(auto &i:a)
#define yesno(x) cout<<(x?"YES":"NO")<<endl
struct pii {
int x, y;
bool operator<(const pii &a) const { return x == a.x ? y < a.y : x < a.x; }
bool operator>(const pii &a) const { return x == a.x ? y > a.y : x > a.x; }
bool operator==(const pii &a) const { return x == a.x && y == a.y; }
bool operator!=(const pii &a) const { return x != a.x || y != a.y; }
pii operator+(const pii &a) const { return {x+a.x, y+a.y}; }
pii operator-(const pii &a) const { return {x-a.x, y-a.y}; }
pii operator*(const int &a) const { return {x*a, y*a}; }
pii operator/(const int &a) const { return {x/a, y/a}; }
void operator+=(const pii &a) { x += a.x; y += a.y; }
void operator-=(const pii &a) { x -= a.x; y -= a.y; }
void operator*=(const int &a) { x *= a; y *= a; }
void operator/=(const int &a) { x /= a; y /= a; }
friend ostream& operator<<(ostream &os, const pii &p) {return os << "(" << p.x << ", " << p.y << ")";}
friend istream& operator>>(istream &is, pii &p) {return is >> p.x >> p.y;}
};
struct pll {
ll x, y;
bool operator<(const pll &a) const { return x == a.x ? y < a.y : x < a.x; }
bool operator>(const pll &a) const { return x == a.x ? y > a.y : x > a.x; }
bool operator==(const pll &a) const { return x == a.x && y == a.y; }
bool operator!=(const pll &a) const { return x != a.x || y != a.y; }
pll operator+(const pll &a) const { return {x+a.x, y+a.y}; }
pll operator-(const pll &a) const { return {x-a.x, y-a.y}; }
pll operator*(const ll &a) const { return {x*a, y*a}; }
pll operator/(const ll &a) const { return {x/a, y/a}; }
void operator+=(const pll &a) { x += a.x; y += a.y; }
void operator-=(const pll &a) { x -= a.x; y -= a.y; }
void operator*=(const ll &a) { x *= a; y *= a; }
void operator/=(const ll &a) { x /= a; y /= a; }
friend ostream& operator<<(ostream &os, const pll &p) {return os << "(" << p.x << ", " << p.y << ")";}
friend istream& operator>>(istream &is, pll &p) {return is >> p.x >> p.y;}
};
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x^(x>>30))*0xbf58476d1ce4e5b9;
x = (x^(x>>27))*0x94d049bb133111eb;
return x^(x>>31);
}
struct custom_hash {
static const uint64_t FIXED_RANDOM;
size_t operator()(uint64_t x) const {return splitmix64(x + FIXED_RANDOM);}
template<typename T> size_t operator()(const T& t) const {return splitmix64(uint64_t(std::hash<T>{}(t)) + FIXED_RANDOM);}
};
const uint64_t custom_hash::FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
mt19937 rng(custom_hash::FIXED_RANDOM);
template<typename K, typename V> using umap = unordered_map<K, V, custom_hash>;
template<typename K> using uset = unordered_set<K, custom_hash>;
template<typename T> using umset = unordered_multiset<T, custom_hash>;
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
template<class T> struct RMiQ {
vvt<T> jmp;
RMiQ(const vt<T>& V) : jmp(1, V) {
for (int pw = 1, k = 1; pw * 2 <= sz(V); pw *= 2, ++k) {
jmp.emplace_back(sz(V) - pw * 2 + 1);
rep(j,0,sz(jmp[k]))
jmp[k][j] = min(jmp[k - 1][j], jmp[k - 1][j + pw]);
}
}
RMiQ() = default;
// 0-indexed, [a,b)
T query(int a, int b) {
assert(a < b); // or return inf if a == b
int dep = 31 - __builtin_clz(b - a);
return min(jmp[dep][a], jmp[dep][b - (1 << dep)]);
}
};
template<class T> struct RMaQ {
vvt<T> jmp;
RMaQ(const vt<T>& V) : jmp(1, V) {
for (int pw = 1, k = 1; pw * 2 <= sz(V); pw *= 2, ++k) {
jmp.emplace_back(sz(V) - pw * 2 + 1);
rep(j,0,sz(jmp[k]))
jmp[k][j] = max(jmp[k - 1][j], jmp[k - 1][j + pw]);
}
}
RMaQ() = default;
// 0-indexed, [a,b)
T query(int a, int b) {
assert(a < b); // or return -inf if a == b
int dep = 31 - __builtin_clz(b - a);
return max(jmp[dep][a], jmp[dep][b - (1 << dep)]);
}
};
int N, M;
bool inc = 1;
int a[200005], b[200005];
RMiQ<int> rmiq;
RMaQ<int> rmaq;
void initialize(vi c, vi d) {
N = sz(c);
M = sz(d);
rep(i,0,N) {
a[i] = c[i];
}
rep(i,0,M) {
b[i] = d[i];
}
rep(i,1,N) {
if (a[i] < a[i-1]) {
inc = 0;
break;
}
}
rmiq = RMiQ<int>(d);
rmaq = RMaQ<int>(d);
return;
}
pii upd(int l, int r, int i) {
int l1 = l, r1 = M-1;
while (l1 < r1) {
int m = (l1+r1+1)/2;
if (rmaq.query(l,m+1) < a[i]) {
l1 = m;
} else {
r1 = m-1;
}
}
r = l1;
l1 = 0, r1 = l;
while (l1 < r1) {
int m = (l1+r1)/2;
if (rmaq.query(m,r+1) < a[i]) {
r1 = m;
} else {
l1 = m+1;
}
}
l = l1;
return {l, r};
}
bool can_reach(int L, int R, int S, int D) {
if (S > D) swap(S, D);
if (inc) {
return a[N-1] > rmaq.query(S,D+1);
} else {
int l = S, r = S,
l2 = D, r2 = D;
bool ok = 0;
rep(i,0,N) {
auto res = upd(l, r, i);
l = res.x;
r = res.y;
res = upd(l2, r2, i);
l2 = res.x;
r2 = res.y;
if (r >= D || l2 <= S) {
ok = 1;
break;
}
if (a[i] <= rmiq.query(l,r+1) || a[i] <= rmiq.query(l2,r2+1)) {
break;
}
}
return ok;
}
}
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