#include<bits/stdc++.h>
#include "game.h"
#define ll long long
#define ff first
#define ss second
#define ln "\n"
using namespace std;
struct SegTree1D{
struct Node{
Node *left, *right;
ll gcd;
Node(){
left=right=nullptr; gcd=0;
}
void populate(){
if (left!=nullptr) return;
left=new Node();
right=new Node();
}
void update(ll tl, ll tr, ll i, ll x, vector<Node*> &leaves){
if (tl==tr){
gcd=x;
leaves[tl]=this;
}else{
populate();
ll tm = (tl+tr)/2;
if (i<=tm) {
left->update(tl, tm, i, x, leaves);
}else{
right->update(tm+1, tr, i, x, leaves);
}
gcd=__gcd(left->gcd, right->gcd);
}
}
ll query(ll tl, ll tr, ll l, ll r){
if (tl==l and tr==r){
return gcd;
}else if (l>r) return 0;
else{
ll tm = (tl+tr)/2;
ll ret=0;
if (left and l<=min(r, tm)) ret=__gcd(ret, left->query(tl, tm, l, min(r, tm)));
if (right and max(l, tm+1)<=r) ret=__gcd(ret, right->query(tm+1, tr, max(l, tm+1), r));
return ret;
}
}
};
vector<Node*> leaves;
Node * root;
ll rsz;
SegTree1D(ll N){
rsz=N;
root=new Node();
leaves.resize(N, nullptr);
}
void update(ll i, ll x){
root->update(0, rsz-1, i, x, leaves);
}
ll query(ll l, ll r){
return root->query(0, rsz-1, l, r);
}
ll getval(ll ind){
if (leaves[ind]==nullptr) return 0;
else return leaves[ind]->gcd;
}
};
struct SegTree2D{
struct mNode{
mNode *left, *right;
SegTree1D *val;
ll csz;
mNode(ll _csz){
csz=_csz;
left=right=nullptr;
val = new SegTree1D(csz);
}
void populate(){
if (!left){
left=new mNode(csz);
right=new mNode(csz);
}
}
void update(ll tl, ll tr, ll i, ll j, ll x){
if (tl==tr){
val->update(j, x);
}else{
populate();
ll tm = (tl+tr)/2;
if (i<=tm){
left->update(tl, tm, i, j, x);
}else{
right->update(tm+1, tr, i, j, x);
}
val->update(j, __gcd(left->val->getval(j), right->val->getval(j)));
}
}
ll query(ll li, ll ri, ll lj, ll rj, ll tl, ll tr){
if (tl==li and tr==ri){
return val->query(lj, rj);
}else if (li>ri) return 0;
else{
ll ret=0;
ll tm = (tl+tr)/2;
if (left and li<=min(ri, tm)) ret=__gcd(ret, left->query(li, min(ri, tm), lj, rj, tl, tm));
if (right and max(li, tm+1)<=ri) ret=__gcd(ret, right->query(max(li, tm+1), ri, lj, rj, tm+1, tr));
return ret;
}
}
};
mNode * root;
ll csz, rsz;
void init(ll R, ll C){
rsz=R; csz=C;
root = new mNode(csz);
}
void update(ll i, ll j, ll x){
root->update(0, rsz-1, i, j, x);
}
ll query(ll li, ll ri, ll lj, ll rj){
return root->query(li, ri, lj, rj, 0, rsz-1);
}
} DS;
void init(int R, int C) {
DS.init(R, C);
}
void update(int P, int Q, long long K) {
DS.update(P, Q, K);
}
long long calculate(int P, int Q, int U, int V) {
/* ... */
return DS.query(P, U, Q, V);
}
