#include<bits/stdc++.h>
#include <type_traits>
#include "game.h"
#define ll long long
#define ff first
#define ss second
#define ln "\n"
using namespace std;
struct SegTree1D{
struct Node{
ll left, right, val;
Node(){
left=right=-1;
val=0;
}
};
vector<Node> nodes;
ll add_node(){
nodes.push_back(Node());
return nodes.size()-1;
}
map<int, ll> leaves;
int rsz;
SegTree1D(int N){
rsz=N;
add_node();
}
void update(ll tl, ll tr, ll v, ll i, ll x){
if (tl==tr){
nodes[v].val=x;
leaves[tl]=v;
}else{
ll tm = (tl+tr)/2;
if (i<=tm){
if (nodes[v].left==-1) nodes[v].left=add_node();
update(tl, tm, nodes[v].left, i, x);
}else{
if (nodes[v].right==-1) nodes[v].right=add_node();
update(tm+1, tr, nodes[v].right, i, x);
}
nodes[v].val=0;
if (nodes[v].left!=-1) nodes[v].val=__gcd(nodes[nodes[v].left].val, nodes[v].val);
if (nodes[v].right!=-1) nodes[v].val=__gcd(nodes[nodes[v].right].val, nodes[v].val);
}
}
void update(ll i, ll x){
update(0, rsz-1, 0, i, x);
}
ll query(ll tl, ll tr, ll v, ll l, ll r){
if (tl==l and tr==r){
return nodes[v].val;
}
else if (l>r) return 0;
else{
ll tm = (tl+tr)/2;
ll res=0;
if (nodes[v].left!=-1) res=__gcd(res, query(tl, tm, nodes[v].left, l, min(r, tm)));
if (nodes[v].right!=-1) res=__gcd(res, query(tm+1, tr, nodes[v].right, max(l, tm+1), r));
return res;
}
}
ll query(int l, int r){
return query(0, rsz-1, 0, l, r);
}
ll getval(int ind){
if (!leaves.count(ind)) return 0;
return nodes[leaves[ind]].val;
}
};
struct SegTree2D{
struct mNode{
mNode *left, *right;
SegTree1D *val;
int csz;
mNode(int _csz){
csz=_csz;
left=right=nullptr;
val = new SegTree1D(csz);
}
void update(int tl, int tr, int i, int j, ll x){
if (tl==tr){
val->update(j, x);
}else{
int tm = (tl+tr)/2;
if (i<=tm){
if (!left) left=new mNode(csz);
left->update(tl, tm, i, j, x);
}else{
if (!right) right=new mNode(csz);
right->update(tm+1, tr, i, j, x);
}
val->update(j, __gcd((left?left->val->getval(j):0), (right?right->val->getval(j):0)));
}
}
ll query(int li, int ri, int lj, int rj, int tl, int tr){
if (tl==li and tr==ri){
return val->query(lj, rj);
}else if (li>ri) return 0;
else{
ll ret=0;
int 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(int R, int C){
rsz=R; csz=C;
root = new mNode(csz);
}
void update(int i, int j, ll x){
root->update(0, rsz-1, i, j, x);
}
ll query(int li, int ri, int lj, int 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);
}
