#include <bits/stdc++.h>
using namespace std;
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<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 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
#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 = 2e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
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; }
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
constexpr int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0
int fstTrue(function<bool(int)> f, int lo, int hi) {
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
int mid = (lo+hi)/2;
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
template<class T> void remDup(vector<T>& v) {
sort(all(v)); v.erase(unique(all(v)),end(v)); }
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> 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); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
template<class A> str ts(complex<A> 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; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
return "("+ts(p.f)+", "+ts(p.s)+")"; }
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << ts(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif
// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string 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
}
#include "game.h"
/**
* Description: Easy BBST. Use split and merge to implement insert and delete.
* Time: O(\log N)
* Source: https://cp-algorithms.com/data_structures/treap.html + others. Also consider
* https://codeforces.com/contest/1340/submission/77861280 (no pointers -> faster)
* https://codeforces.com/contest/1340/submission/77852254 (shared_ptr -> destroyed when nothing refers to it)
* Verification: http://www.spoj.com/problems/ORDERSET/
*/
typedef struct tnode* pt;
struct tnode {
int pri; pt c[2]; // essential
int pos; ll val, sum;
tnode (int _pos, ll _val) {
pri = rng(); c[0] = c[1] = NULL;
pos = _pos, val = sum = _val;
}
};
ll getSum(pt x) { return x?x->sum:0; } // OK
ll co(ll a, ll b) { return __gcd(a,b); } // OK
pt calc(pt x) {
x->sum = co(x->val,co(getSum(x->c[0]),getSum(x->c[1])));
return x; }
// void tour(pt x, vi& v) { // print values of nodes,
// if (!x) return; // inorder traversal
// tour(x->c[0],v); v.pb(x->val); tour(x->c[1],v);
// }
pair<pt,pt> split(pt t, int v) { // >= v goes to the right
if (!t) return {t,t};
if (t->pos >= v) {
auto p = split(t->c[0], v); t->c[0] = p.s;
return {p.f,calc(t)};
} else {
auto p = split(t->c[1], v); t->c[1] = p.f;
return {calc(t),p.s};
}
}
pt merge(pt l, pt r) { // merge treaps, keys in left < keys in right
if (!l || !r) return l?:r;
pt t;
if (l->pri > r->pri) l->c[1] = merge(l->c[1],r), t = l;
else r->c[0] = merge(l,r->c[0]), t = r;
return calc(t);
}
pt ins(pt x, int pos, ll val) { // insert v
auto a = split(x,pos), b = split(a.s,pos+1);
//dbg("SPLIT");
return merge(a.f,merge(new tnode(pos,val),b.s)); }
void INS(pt& x, int pos, ll val) {
//dbg("INS",pos,val);
x = ins(x,pos,val);
//dbg("DONEINS");
}
ll searchLef(pt p, int L) {
if (!p) return 0;
if (p->pos < L) return searchLef(p->c[1],L);
return co(p->val,co(searchLef(p->c[0],L),getSum(p->c[1])));
}
ll searchRig(pt p, int R) {
if (!p) return 0;
if (p->pos > R) return searchRig(p->c[0],R);
return co(p->val,co(searchRig(p->c[1],R),getSum(p->c[0])));
}
ll search(pt p, int L, int R) {
if (!p) return 0;
if (p->pos < L) return search(p->c[1],L,R);
if (p->pos > R) return search(p->c[0],L,R);
return co(p->val,co(searchLef(p->c[0],L),searchRig(p->c[1],R)));
}
typedef struct Node* pN;
struct Node {
pt d; pN l,r;
Node() { d = NULL; l = r = NULL; }
};
pN root = NULL;
void init(int R, int C) {
/* ... */
}
void tri(ll& a, ll b) { a = co(a,b); } // OK
void upd(int P, int Q, ll K, pN& cur, int L = 0, int R = 1e9) {
if (!cur) cur = new Node();
if (L == R) return INS(cur->d,Q,K);
int M = (L+R)/2;
if (P <= M) upd(P,Q,K,cur->l,L,M);
else upd(P,Q,K,cur->r,M+1,R);
ll g = 0;
if (cur->l) tri(g,search(cur->l->d,Q,Q));
if (cur->r) tri(g,search(cur->r->d,Q,Q));
//dbg("OOPS",g);
INS(cur->d,Q,g);
}
void update(int P, int Q, long long K) {
//dbg("UPDATE");
upd(P,Q,K,root); }
ll query(int P, int U, int Q, int V, pN cur, int L = 0, int R = 1e9) {
if (!cur || R < P || U < L) return 0; // OK
if (P <= L && R <= U) return search(cur->d,Q,V);
int M = (L+R)/2;
return __gcd(query(P,U,Q,V,cur->l,L,M),query(P,U,Q,V,cur->r,M+1,R));
}
long long calculate(int P, int Q, int U, int V) {
//dbg("QUERY");
return query(P,U,Q,V,root);
}
