//#pragma GCC optimize("Ofast,avx2")
#include "game.h"
#include <numeric>
#define ll long long
#define OUT 0
#define merge gcd
using namespace std;
const int N = (1<<30);
struct ynode {
ynode() : val(OUT), left(nullptr), right(nullptr) {}
ll val = OUT;
ynode *left, *right;
};
struct xnode {
xnode() : left(nullptr), right(nullptr), yy(ynode()) {}
xnode *left, *right;
ynode yy;
} *root;
ll query_y(const int &qy1, const int &qy2, const 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(const int &qx1, const int &qy1, const int &qx2, const int &qy2, const 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(const int &qy, const 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->val = merge((node->left ? node->left->val : OUT), (node->right ? node->right->val : OUT));
}
void update_x(const int &qx, const int &qy, const ll &val, xnode* node, int l = 0, int r = N - 1)
{
if (l == r) {
update_y(qy, val, &node->yy);
return;
}
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 ? query_y(qy, qy, &node->left->yy) : OUT),
(node->right ? query_y(qy, qy, &node->right->yy) : OUT)
), &node->yy);
}
void init(int R, int C) { root = new xnode(); }
void update(int x, int y, long long k) { update_x(x, y, k, root); }
long long calculate(int x1, int y1, int x2, int y2) { return query_x(x1, y1, x2, y2, root); }
