#include "game.h"
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int N = 1e9 + 1;
const ll OUT = 0;
ll merge(ll t1, ll t2) {
return gcd(t1, t2);
}
struct ynode {
ll val = OUT;
ynode* left = nullptr, * right = nullptr;
inline void upd() {
ll m1 = OUT, m2 = OUT;
if (left) m1 = left->val;
if (right) m2 = right->val;
val = merge(m1, m2);
}
};
struct xnode {
xnode* left = nullptr, * right = nullptr;
ynode* yy = new ynode();
};
ll query_y(int qy1, int qy2, ynode* node, int l = 0, int r = N - 1)
{
if (node == nullptr || r < qy1 || qy2 < l) return OUT;
if (qy1 <= l && r <= qy2) return node->val;
const int mid = (l + r) / 2;
return merge(
query_y(qy1, qy2, node->left, l, mid),
query_y(qy1, qy2, node->right, mid + 1, r)
);
}
ll query_x(int qx1, int qy1, int qx2, int qy2, xnode* node, int l = 0, int r = N - 1)
{
if (node == nullptr || r < qx1 || qx2 < l) return OUT;
if (qx1 <= l && r <= qx2) return query_y(qy1, qy2, node->yy);
const int mid = (l + r) / 2;
return merge(
query_x(qx1, qy1, qx2, qy2, node->left, l, mid),
query_x(qx1, qy1, qx2, qy2, node->right, mid + 1, r)
);
}
void update_y(int qy, ll val, ynode* node, int l = 0, int r = N - 1)
{
if (l == r) {
node->val = val;
return;
}
const int mid = (l + r) / 2;
if (qy <= mid) {
if (!node->left) node->left = new ynode();
update_y(qy, val, node->left, l, mid);
}
else {
if (!node->right) node->right = new ynode();
update_y(qy, val, node->right, mid + 1, r);
}
node->upd();
}
void update_x(int qx, int qy, ll val, xnode* node, int l = 0, int r = N - 1)
{
if (l != r) {
const int mid = (l + r) / 2;
if (qx <= mid) {
if (!node->left) node->left = new xnode();
update_x(qx, qy, val, node->left, l, mid);
}
else {
if (!node->right) node->right = new xnode();
update_x(qx, qy, val, node->right, mid + 1, r);
}
}
update_y(qy, merge(
(node->left && node->left->yy ? query_y(qy, qy, node->left->yy) : OUT),
(node->right && node->right->yy ? query_y(qy, qy, node->right->yy) : OUT)
), node->yy);
}
xnode* root;
void init(int R, int C) { root = new xnode(); }
void update(int x, int y, ll k) { update_x(x, y, k, root); }
ll calculate(int x1, int y1, int x2, int y2) { return query_x(x1, y1, x2, y2, root); }
