#include "game.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define fi first
#define se second
#define ll long long
#define ld long double
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define mpp make_pair
#define ve vector
using namespace std;
using namespace __gnu_pbds;
template<class T> using oset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
const ll inf = 1e18; const int iinf = 1e9;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T> inline bool chmin(T& a, T b) { return (a > b ? a = b, 1 : 0); }
template <typename T> inline bool chmax(T& a, T b) { return (a < b ? a = b, 1 : 0); }
inline ll gcd(const ll &a, const ll &b) { return (!b ? a : gcd(b, a % b)); }
struct node {
node *l = nullptr;
node *r = nullptr;
ll g;
node(ll x = 0) : g(x) {}
};
inline void upd1(node *&v, int vl, int vr, int pos, const ll &x) {
// cout << "getting " << pos << " on [" << vl << ", " << vr << "]" << '\n';
if (!v) v = new node();
if (vl == vr) return void(v->g = x);
int m = vl + vr >> 1;
if (pos <= m) upd1(v->l, vl, m, pos, x);
else upd1(v->r, m + 1, vr, pos, x);
v->g = gcd(!v->l ? 0 : v->l->g, !v->r ? 0 : v->r->g);
}
inline ll get1(node *v, int vl, int vr, int l, int r) {
// cout << "getting " << l << ", " << r << " on [" << vl << ", " << vr << "]" << '\n';
if (l > r || !v) return 0ll;
else if (vl == l && vr == r) return v->g;
int m = vl + vr >> 1;
return gcd(get1(v->l,vl,m,l,min(r,m)),
get1(v->r,m+1,vr,max(l,m+1),r));
}
inline void rec1(node *&v, node *a, node *b, int vl, int vr, int pos) {
if (!v) v = new node();
v->g = gcd(!a ? 0 : a->g, !b ? 0 : b->g);
if (vl == vr) return;
int m = vl + vr >> 1;
if (pos <= m) rec1(v->l, !a ? nullptr : a->l, !b ? nullptr : b->l, vl, m, pos);
else rec1(v->r, !a ? nullptr : a->r, !b ? nullptr : b->r, m + 1, vr, pos);
}
inline void dbg(node *v, int vl, int vr, int lx, int rx) {
cout << "[" << lx << ", " << rx << "] * [" << vl << ", " << vr << "]: " << (!v ? 0 : v->g) << '\n';
if (vl == vr) return;
int m = vl + vr >> 1;
dbg(!v ? nullptr : v->l, vl, m, lx, rx);
dbg(!v ? nullptr : v->r, m + 1, vr, lx, rx);
}
int l1, r1, l2, r2;
struct Node {
Node *l = nullptr;
Node *r = nullptr;
node *st = nullptr;
Node() {}
}; Node *t = new Node();
inline void upd(Node *&v, int vl, int vr, int x, int y, ll d) {
if (!v) v = new Node();
if (vl == vr) {
upd1(v->st, l2, r2, y, d);
return;
}
int m = vl + vr >> 1;
if (x <= m) upd(v->l, vl, m, x, y, d);
else upd(v->r, m + 1, vr, x, y, d);
rec1(v->st, !v->l ? nullptr : v->l->st, !v->r ? nullptr : v->r->st, l2, r2, y);
}
inline ll get(Node *v, int vl, int vr, int lx, int rx, int ly, int ry) {
if (lx > rx || !v) return 0ll;
else if (vl == lx && vr == rx) return get1(v->st, l2, r2, ly, ry);
int m = vl + vr >> 1;
return gcd(get(v->l,vl,m,lx,min(rx,m),ly,ry),
get(v->r,m+1,vr,max(lx,m+1),rx,ly,ry));
}
void init(int R, int C) {
l1 = 0, r1 = R - 1;
l2 = 0, r2 = C - 1;
}
void update(int P, int Q, long long K) {
upd(t, l1, r1, P, Q, K);
}
long long calculate(int P, int Q, int U, int V) {
return get(t, l1, r1, P, U, Q, V);
}
