#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif
/*
already knew the solution idea (dynamic segtree with a treap/dynamic segtree in each node)
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "game.h"
struct dynamic_segtree{
struct node{
node *l = nullptr, *r = nullptr;
ll g = 0;
node(){
}
node(ll x){
g = x;
}
};
node* root;
int n;
dynamic_segtree(){
}
dynamic_segtree(int n_){
n = n_;
root = new node();
}
void pupd(node* &u, int lx, int rx, int i, ll v){
if(!u) u = new node();
if(rx-lx == 1){
u->g = v;
return;
}
int mid = (lx+rx) >> 1;
if(i < mid){
pupd(u->l,lx,mid,i,v);
}
else{
pupd(u->r,mid,rx,i,v);
}
u->g = 0;
if(u->l) u->g = gcd(u->g,u->l->g);
if(u->r) u->g = gcd(u->g,u->r->g);
}
void pupd(int i, ll v){
pupd(root,0,n,i,v);
}
ll query(node* u, int lx, int rx, int l, int r){
if(!u) return 0;
if(lx >= r or rx <= l) return 0;
if(lx >= l and rx <= r) return u->g;
int mid = (lx+rx) >> 1;
return gcd(query(u->l,lx,mid,l,r),query(u->r,mid,rx,l,r));
}
ll query(ll l, ll r){
return query(root,0,n,l,r+1);
}
};
struct seg2d{
int n,m;
struct node{
node *l = nullptr, *r = nullptr;
dynamic_segtree st;
node(int m_){
st = dynamic_segtree(m_);
}
};
node* root;
seg2d(){
}
seg2d(int n_, int m_){
n = n_, m = m_;
root = new node(m);
}
void pupd(node* &u, int lx, int rx, int i, int j, ll v){
if(!u) u = new node(m);
if(rx-lx == 1){
u->st.pupd(j,v);
return;
}
int mid = (lx+rx) >> 1;
if(i < mid){
pupd(u->l,lx,mid,i,j,v);
}
else{
pupd(u->r,mid,rx,i,j,v);
}
ll g = 0;
if(u->l) g = u->l->st.query(j,j);
if(u->r) g = gcd(g,u->r->st.query(j,j));
u->st.pupd(j,g);
}
void pupd(int i, int j, ll v){
pupd(root,0,n,i,j,v);
}
ll query(node* u, int lx, int rx, int l, int r, int x, int y){
if(!u) return 0;
if(lx >= r or rx <= l) return 0;
if(lx >= l and rx <= r) return u->st.query(x,y);
int mid = (lx+rx) >> 1;
return gcd(query(u->l,lx,mid,l,r,x,y),query(u->r,mid,rx,l,r,x,y));
}
ll query(int l, int r, int x, int y){
return query(root,0,n,l,r+1,x,y);
}
};
seg2d st;
void init(int n, int m) {
st = seg2d(n,m);
}
void update(int i, int j, long long v) {
st.pupd(i,j,v);
}
long long calculate(int l1, int l2, int r1, int r2) {
return st.query(l1,r1,l2,r2);
}
