//#include <iostream> //cin, cout
#include "game.h"
/*
#include <fstream>
std::ifstream cin ("ex.in");
std::ofstream cout ("ex.out");
*/
// includes
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <string>
#include <vector>
#include <array>
#include <algorithm>
#include <numeric>
#include <iomanip>
#include <unordered_set>
#include <stack>
#include <ext/pb_ds/assoc_container.hpp>
#include <random>
#include <chrono>
//usings
using namespace std;
using namespace __gnu_pbds;
// misc
#define ll long long
#define pb push_back
#define pq priority_queue
#define ub upper_bound
#define lb lower_bound
template<typename T, typename U> bool emin(T &a, const U &b){ return b < a ? a = b, true : false; }
template<typename T, typename U> bool emax(T &a, const U &b){ return b > a ? a = b, true : false; }
typedef uint64_t hash_t;
// vectors
#define vi vector<int>
#define vvi vector<vi>
#define vvvi vector<vvi>
#define vpii vector<pair<int, int>>
#define vvpii vector<vector<pair<int, int>>>
#define vppipi vector<pair<int, pair<int, int>>>
#define vl vector<ll>
#define vvl vector<vl>
#define vvvl vector<vvl>
#define vpll vector<pair<ll, ll>>
#define vb vector<bool>
#define vvb vector<vb>
#define vs vector<string>
#define sz(x) (int)x.size()
#define rz resize
#define all(x) x.begin(), x.end()
// pairs
#define pii pair<int, int>
#define pll pair<ll, ll>
#define mp make_pair
#define f first
#define s second
// sets
#define si set<int>
#define sl set<ll>
#define ss set<string>
#define in insert
template <class T> using iset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
// maps
#define mii map<int, int>
#define mll map<ll, ll>
// loops
#define FR(x, z, y) for (int x = z; x < y; x++)
#define FRe(x, z, y) FR(x, z, y + 1)
#define F(x, y) FR(x, 0, y)
#define Fe(x, y) F(x, y + 1)
#define A(x, y) for(auto &x : y)
int Y, X;
struct Xnode{
Xnode(int x, int y) : l(x), r(y), v(0), lc(NULL), rc(NULL) {}
int l, r;
ll v;
Xnode *lc, *rc;
};
struct Ynode{
Ynode() : kid(1, X), lc(NULL), rc(NULL) {}
Xnode kid;
Ynode *lc, *rc;
} *root;
ll gcd2(ll x, ll y){
if(y == 0) return x;
return gcd2(y, x % y);
}
void upd2(Xnode *cur, int x, ll k){
int l = cur->l, r = cur->r, m = (l + r) / 2;
if(l == r) {
cur->v = k;
return;
}
Xnode **kid = &(x <= m ? cur->lc : cur->rc);
if(*kid == NULL){
*kid = new Xnode(x, x);
(*kid)->v = k;
} else if((*kid)->l <= x && x <= (*kid)->r){
upd2(*kid, x, k);
} else {
do{
if(x <= m) r = m;
else l = m + 1;
m = (r + l) / 2;
} while ((x <= m) == ((*kid)->r <= m));
Xnode *ncur = new Xnode(l, r);
if((*kid)->r <= m) ncur->lc = *kid;
else ncur->rc = *kid;
*kid = ncur;
upd2(*kid, x, k);
}
cur->v = gcd2(cur->lc ? cur->lc->v : 0, cur->rc ? cur->rc->v : 0);
}
ll get2(Xnode *cur, int rl, int rr){
if(cur == NULL || cur->l > rr || cur->r < rl) return 0;
if(rl <= cur->l && cur->r <= rr) return cur->v;
return gcd2(get2(cur->lc, rl, rr), get2(cur->rc, rl, rr));
}
void upd1(Ynode *cur, int l, int r, int y, int x, ll k){
if(l == r) {
upd2(&cur->kid, x, k);
return;
}
int m = (l + r) / 2;
if(y <= m){
if(cur->lc == NULL) cur->lc = new Ynode;
upd1(cur->lc, l, m, y, x, k);
} else {
if(cur->rc == NULL) cur->rc = new Ynode;
upd1(cur->rc, m + 1, r, y, x, k);
}
ll z = gcd2(cur->lc ? get2(&cur->lc->kid, x, x) : 0, cur->rc ? get2(&cur->rc->kid, x, x) : 0);
upd2(&cur->kid, x, z);
}
ll get1(Ynode *cur, int l, int r, int rl, int rr, int xl, int xr){
if(cur == NULL || r < rl || l > rr) return 0;
if(rl <= l && r <= rr) return get2(&cur->kid, xl, xr);
int m = (l + r) / 2;
return gcd2(get1(cur->lc, l, m, rl, rr, xl, xr), get1(cur->rc, m + 1, r, rl, rr, xl, xr));
}
void init(int R, int C){
Y = R, X = C;
root = new Ynode;
}
void update(int P, int Q, ll K){
P++; Q++;
upd1(root, 1, Y, P, Q, K);
}
ll calculate(int P, int Q, int U, int V){
P++; Q++; U++; V++;
return get1(root, 1, Y, P, U, Q, V);
}
