#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"
typedef struct node* pn;
struct node {
ll d; pn l,r; int L, R;
node(ll _d, int _L, int _R) : d(_d), L(_L), R(_R) { l = r = NULL; }
};
typedef struct Node* pN;
struct Node {
pn 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 = __gcd(a,b); } // OK
void UPD(pi P, int Q, ll K, pn& cur, int L = 0, int R = 1e9) {
if (!cur) { cur = new node(K,Q,Q); return; } // OK
//dbg("UPDATE",P,mp(cur->L,cur->R),Q,K,L,R);
if (cur->L <= Q && Q <= cur->R) {
if (cur->L == cur->R) { cur->d = K; return; }
int M = (cur->L+cur->R)/2;
if (Q <= M) UPD(P,Q,K,cur->l,cur->L,M);
else UPD(P,Q,K,cur->r,M+1,cur->R);
cur->d = __gcd(cur->l?cur->l->d:0,cur->r?cur->r->d:0);
return;
}
while (1) {
int M = (L+R)/2;
if ((Q <= M) != (cur->L <= M)) break;
if (Q <= M) R = M;
else L = M+1;
}
pn x = cur, y = new node(K,Q,Q);
if (cur->L > Q) swap(x,y);
int M = (L+R)/2;
assert(L <= x->L && x->R <= M && M < y->L && y->R <= R);
cur = new node(__gcd(x->d,y->d),L,R);
cur->l = x, cur->r = y;
}
ll QUERY(pi P, int Q, int V, pn cur) {
if (!cur || cur->R < Q || V < cur->L) return 0;
if (Q <= cur->L && cur->R <= V) {
// dbg("QUERY",P,mp(cur->L,cur->R),Q,V,cur->d);
// if (cur->l) dbg("LEF",cur->l->d);
// if (cur->r) dbg("RIG",cur->r->d,cur->r->L,cur->r->R);
return cur->d;
}
return __gcd(QUERY(P,Q,V,cur->l),QUERY(P,Q,V,cur->r));
}
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 UPD({L,R},Q,K,cur->d);
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) g = __gcd(g,QUERY({L,R},Q,Q,cur->l->d));
if (cur->r) g = __gcd(g,QUERY({L,R},Q,Q,cur->r->d));
//dbg("OKUPDATE",mp(L,R),Q,g);
UPD({L,R},Q,g,cur->d);
}
void update(int P, int Q, long long K) {
//dbg("UPDATE",P,Q,K);
upd(P,Q,K,root); }
int P,U,Q,V;
ll query(pN cur, int L = 0, int R = 1e9) {
if (!cur || R < P || U < L) return 0; // OK
if (P <= L && R <= U) return QUERY({L,R},Q,V,cur->d);
int M = (L+R)/2;
return __gcd(query(cur->l,L,M),query(cur->r,M+1,R));
}
long long calculate(int _P, int _Q, int _U, int _V) {
P = _P, Q = _Q, U = _U, V = _V;
//dbg("QUERY");
return query(root);
}
