#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include "game.h"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#define endl "\n"
#define ll long long
#define mp make_pair
#define ins insert
#define lb lower_bound
#define pb push_back
#define ub upper_bound
#define lll __int128
#define fi first
#define se second
using namespace std;
using namespace __gnu_pbds;
typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_multiset;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
const int lim = 1e9 + 5;
long long gcd2(long long X, long long Y) {
long long tmp;
while (X != Y && Y != 0) {
tmp = X;
X = Y;
Y = tmp % Y;
}
return X;
}
struct node {
int l = -1, r = -1, nx = -1;
ll val = 0;
};
struct segtree {
vector<node> v;
segtree() {
v.pb(node());
v.pb(node());
}
int add_node() {
v.pb(node());
return v.size() - 1;
}
void update_node(int nd) {
v[nd].val = 0;
if(v[nd].l != -1)
v[nd].val = gcd2(v[v[nd].l].val, v[nd].val);
if(v[nd].r != -1)
v[nd].val = gcd2(v[v[nd].r].val, v[nd].val);
}
void update_x(int x, int y, ll val) {
int nd = 1, cl = 0, cr = lim - 1;
if(v[nd].nx == -1)
v[nd].nx = add_node();
update_y(v[nd].nx, y, val);
while(cl < cr) {
int mid = (cl + cr) >> 1;
if(x <= mid) {
cr = mid;
if(v[nd].l == -1)
v[nd].l = add_node();
nd = v[nd].l;
}
else {
cl = mid + 1;
if(v[nd].r == -1)
v[nd].r = add_node();
nd = v[nd].r;
}
if(v[nd].nx == -1)
v[nd].nx = add_node();
update_y(v[nd].nx, y, val);
}
}
void update_y(int nd, int y, ll val) {
int cl = 0, cr = lim - 1;
vector<int> nodes = {nd};
while(cl < cr) {
int mid = (cl + cr) >> 1;
if(y <= mid) {
cr = mid;
if(v[nd].l == -1)
v[nd].l = add_node();
nd = v[nd].l;
}
else {
cl = mid + 1;
if(v[nd].r == -1)
v[nd].r = add_node();
nd = v[nd].r;
}
nodes.pb(nd);
}
v[nd].val = val;
nodes.pop_back();
reverse(nodes.begin(), nodes.end());
for(auto x : nodes) {
// cerr << "UPDATE " << x << endl;
update_node(x);
}
}
ll query_x(int nd, int cl, int cr, int l, int r, int y1, int y2) {
if(nd == -1 || cl > r || cr < l)
return 0;
else if(cl >= l && cr <= r) {
// cerr << "GET Y " << cl << " " << cr << endl;
// cerr << l << " " << r << " " << y1 << " " << y2 << endl;
return query_y(v[nd].nx, 0, lim - 1, y1, y2);
}
else {
int mid = (cl + cr) >> 1;
return gcd2(query_x(v[nd].l, cl, mid, l, r, y1, y2), query_x(v[nd].r, mid + 1, cr, l, r, y1, y2));
}
}
ll query_y(int nd, int cl, int cr, int l, int r) {
if(nd == -1 || cl > r || cr < l)
return 0;
else if(cl >= l && cr <= r) {
// cerr << "GOT Y " << nd << " " << cl << " " << cr << " " << v[nd].val << endl;
return v[nd].val;
}
else {
int mid = (cl + cr) >> 1;
return gcd2(query_y(v[nd].l, cl, mid, l, r), query_y(v[nd].r, mid + 1, cr, l, r));
}
}
};
segtree seg;
void init(int R, int C) {
seg.v.clear();
seg.v.pb(node());
seg.v.pb(node());
}
void update(int P, int Q, long long K) {
seg.update_x(P, Q, K);
}
long long calculate(int P, int Q, int U, int V) {
return seg.query_x(1, 0, lim - 1, P, U, Q, V);
}
