#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <iostream>
#include <iomanip>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<db, db> pd;
typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#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 resz 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
#define f1r(i, a, b) for (int i = (a); i < (b); ++i)
#define f0r(i, a) f1r(i, 0, a)
#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)
mt19937 rng((uint32_t) chrono::steady_clock::now().time_since_epoch().count());
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> using V = vector<T>;
#ifdef LOCAL
#define dbg(...) debug(#__VA_ARGS__, __VA_ARGS__);
#else
#define dbg(...) 17;
#endif
template<typename T, typename S> ostream& operator << (ostream &os, const pair<T, S> &p) { return os << "(" << p.first << ", " << p.second << ")"; }
template<typename C, typename T = decay<decltype(*begin(declval<C>()))>, typename enable_if<!is_same<C, string>::value>::type* = nullptr>
ostream& operator << (ostream &os, const C &c) { bool f = true; os << "{"; for (const auto &x : c) { if (!f) os << ", "; f = false; os << x; } return os << "}"; }
template<typename T> void debug(string s, T x) { cerr << s << " = " << x << "\n"; }
template<typename T, typename... Args> void debug(string s, T x, Args... args) { cerr << s.substr(0, s.find(',')) << " = " << x << " | "; debug(s.substr(s.find(',') + 2), args...); }
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31 - __builtin_clz(x); } // floor(log2(x))
namespace input {
template<class T> void re(complex<T>& x);
template<class T1, class T2> void re(pair<T1, T2>& p);
template<class T> void re(vector<T>& a);
template<class T, int SZ> void re(array<T, SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(double& x) { string t; re(t); x = stod(t); }
void re(ld& x) { string t; re(t); x = stold(t); }
template<class T, class... Ts> void re(T& t, Ts&... ts) {
re(t); re(ts...); }
template<class T> void re(complex<T>& x) { T a, b; re(a, b); x = cd(a, b); }
template<class T1, class T2> void re(pair<T1, T2>& p) { re(p.f, p.s); }
template<class T> void re(vector<T>& a) { F0R(i, sz(a)) re(a[i]); }
template<class T, int SZ> void re(array<T, SZ>& a) { F0R(i, SZ) re(a[i]); }
}
using namespace input;
namespace output {
void pr(int x) { cout << x; }
void pr(long x) { cout << x; }
void pr(ll x) { cout << x; }
void pr(unsigned x) { cout << x; }
void pr(unsigned long x) { cout << x; }
void pr(unsigned long long x) { cout << x; }
void pr(float x) { cout << x; }
void pr(double x) { cout << x; }
void pr(ld x) { cout << x; }
void pr(char x) { cout << x; }
void pr(const char* x) { cout << x; }
void pr(const string& x) { cout << x; }
void pr(bool x) { pr(x ? "true" : "false"); }
template<class T> void pr(const complex<T>& x) { cout << x; }
template<class T1, class T2> void pr(const pair<T1, T2>& x);
template<class T> void pr(const T& x);
template<class T, class... Ts> void pr(const T& t, const Ts&... ts) {
pr(t); pr(ts...); }
template<class T1, class T2> void pr(const pair<T1,T2>& x) {
pr("{", x.f, ", ", x.s, "}"); }
template<class T> void pr(const T& x) {
pr("{"); // const iterator needed for vector<bool>
bool fst = 1; for (const auto& a: x) pr(!fst ? ", " : "", a), fst = 0;
pr("}"); }
void ps() { pr("\n"); } // print w/ spaces
template<class T, class... Ts> void ps(const T& t, const Ts&... ts) {
pr(t); if (sizeof...(ts)) pr(" "); ps(ts...); }
void pc() { pr("]\n"); } // debug w/ commas
template<class T, class... Ts> void pc(const T& t, const Ts&... ts) {
pr(t); if (sizeof...(ts)) pr(", "); pc(ts...); }
}
using namespace output;
namespace io {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
cin.sync_with_stdio(0); cin.tie(0);
if (sz(s)) { setIn(s + ".in"), setOut(s + ".out"); }
}
}
using namespace io;
const int MOD = 1e9 + 7; // 998244353;
const ld PI = acos((ld) -1);
typedef std::decay <decltype(MOD)>::type mod_t;
struct mi {
mod_t val;
explicit operator mod_t() const { return val; }
mi() { val = 0; }
mi(const long long& v) {
val = (-MOD <= v && v <= MOD) ? v : v % MOD;
if (val < 0) val += MOD; }
friend std::istream& operator >> (std::istream& in, mi& a) {
long long x; std::cin >> x; a = mi(x); return in; }
friend std::ostream& operator << (std::ostream& os, const mi& a) { return os << a.val; }
friend void pr(const mi& a) { pr(a.val); }
friend void re(mi& a) { long long x; cin >> x; a = mi(x); }
friend bool operator == (const mi& a, const mi& b) { return a.val == b.val; }
friend bool operator != (const mi& a, const mi& b) { return !(a == b); }
friend bool operator < (const mi& a, const mi& b) { return a.val < b.val; }
friend bool operator > (const mi& a, const mi& b) { return a.val > b.val; }
friend bool operator <= (const mi& a, const mi& b) { return a.val <= b.val; }
friend bool operator >= (const mi& a, const mi& b) { return a.val >= b.val; }
mi operator - () const { return mi(-val); }
mi& operator += (const mi& m) {
if ((val += m.val) >= MOD) val -= MOD;
return *this; }
mi& operator -= (const mi& m) {
if ((val -= m.val) < 0) val += MOD;
return *this; }
mi& operator *= (const mi& m) { val = (long long) val * m.val % MOD;
return *this; }
friend mi pow(mi a, long long p) {
mi ans = 1; assert(p >= 0);
for (; p; p /= 2, a *= a) if (p & 1) ans *= a;
return ans; }
friend mi inv(const mi& a) { assert(a != 0); return pow(a, MOD - 2); }
mi& operator /= (const mi& m) { return (*this) *= inv(m); }
friend mi operator + (mi a, const mi& b) { return a += b; }
friend mi operator - (mi a, const mi& b) { return a -= b; }
friend mi operator * (mi a, const mi& b) { return a *= b; }
friend mi operator / (mi a, const mi& b) { return a /= b; }
};
typedef pair<mi, mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;
#include "teams.h"
int n;
vi a;
vi b;
vector<vpi> ri;
vector<vpi> le;
void init(int N, int A[], int B[]) {
n = N;
a.resize(n);
b.resize(n);
ri.resize(n+5);
le.resize(n+5);
f0r(i, n) a[i] = A[i], b[i] = B[i];
f0r(i, n) ri[b[i]].eb(a[i], i);
f0r(i, n) le[a[i]].eb(b[i], i);
}
int can(int M, int K[]) {
int m = M;
vi k(m);
f0r(i, m) k[i] = K[i];
set<pi> use;
vi gr(n+5);
f0r(i, m) gr[k[i]]++;
for (int i = n; i >= 1; i--) {
for (auto& x : ri[i]) {
use.emplace(x);
}
f0r(_, gr[i]) {
int x = i;
int need = x;
while (need && sz(use)) {
auto it = *prev(use.end());
use.erase(prev(use.end()));
need--;
}
if (need) {
return 0;
}
}
for (auto& x : le[i]) {
if (use.count({i, x.s}))
use.erase({i, x.s});
}
}
return 1;
}
