#include<bits/stdc++.h>
#include "game.h"
using namespace std;
#define tm (p->tl+p->tr >> 1)
#define mp make_pair
#define pb push_back
#define st first
#define nd second
typedef long long ll;
const int mod = 1e9 + 7;
const int N = 2e5 + 5;
inline ll gcd(ll u, ll v) {
ll r;
while (v != 0) { r = u % v; u = v; v = r; }
return u;
}
struct node{
ll x;
int tl, tr;
struct node *l, *r, *to_y;
node() { x = 0; l = r = to_y = NULL; }
};
node* nw(int l, int r){
node* p = (node*) malloc(sizeof(node));
p -> tl = l; p -> tr = r;
return p;
}
ll qry_y(node* p, int ly, int ry) {
if(ly > p->tr || ry < p->tl) return 0;
if (ly <= p->tl && p->tr <= ry) return p->x;
return gcd(p->l ? qry_y(p->l,ly,ry) : 0 , p->r ? qry_y(p->r,ly,ry) : 0);
}
ll qry_x(node* p, int lx, int rx, int ly, int ry) {
if(lx > p->tr || rx < p->tl) return 0;
if (lx <= p->tl && p->tr <= rx) return p->to_y ? qry_y(p->to_y,ly,ry) : 0;
return gcd(p->l ? qry_x(p->l,lx,rx,ly,ry) : 0 , p->r ? qry_x(p->r,lx,rx,ly,ry) : 0);
}
void up_y(node* p, int py, ll val){
if(p->tl == p->tr){ p->x = val; return; }
if(py > tm) { if(p->r == NULL) p->r = nw(tm+1,p->tr); up_y(p->r,py,val); }
else { if(p->l == NULL) p->l = nw(p->tl,tm); up_y(p->l,py,val); }
p->x = gcd(p->l ? p->l->x : 0 , p->r ? p->r->x : 0);
}
void up_x(node* p, int px, int py, ll val){
if(p->tl < p->tr){
if(px > tm) { if(p->r == NULL) p->r = nw(tm+1,p->tr); up_x(p->r,px,py,val); }
else { if(p->l == NULL) p->l = nw(p->tl,tm); up_x(p->l,px,py,val); }
val = gcd(p->l ? qry_y(p->l->to_y,py,py) : 0 , p->r ? qry_y(p->r->to_y,py,py) : 0);
}
if(p->to_y == NULL) p->to_y = nw(0,mod); up_y(p->to_y,py,val);
}
node* root;
void update(int x, int y, ll val){
up_x(root,x,y,val);
}
ll calculate(int lx, int ly, int rx, int ry){
return qry_x(root,lx,rx,ly,ry);
}
void init(int a, int b) { root = nw(0,mod); }
