#include "game.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
#define debug(x) {cerr<<#x<<"="<<x<<"\n";}
#define debug2(x, y) {cerr<<#x<<", "<<#y<<" = "<<x<<", "<<y<<"\n";}
#define debugp(p) {cerr<<#p" = {"<<p.first<<", "<<p.second<<"}\n";}
#define pb push_back
#define all(x) x.begin(), x.end()
ll gcd2(ll X, ll Y) {
ll tmp;
while (X != Y && Y != 0) {
tmp = X;
X = Y;
Y = tmp % Y;
}
return X;
}
const int SEGSZ=19000000, SEGSZ2=700000;
ll seg[SEGSZ], ans;
int L[SEGSZ], R[SEGSZ], ts;
int Set(int id, int tl, int tr, int pos, ll val){
if (!id) id=++ts;
if (tr-tl==1){
seg[id]=val;
return id;
}
int mid=(tl+tr)>>1;
if (pos<mid) L[id]=Set(L[id], tl, mid, pos, val);
else R[id]=Set(R[id], mid, tr, pos, val);
seg[id]=gcd2(seg[L[id]], seg[R[id]]);
return id;
}
void Get(int id, int tl, int tr, int l, int r, ll &ans){
if (r<=tl || tr<=l || !id) return ;
if (l<=tl && tr<=r){
ans=gcd2(ans, seg[id]); // overall log(10^18) for single query of problem
return ;
}
int mid=(tl+tr)>>1;
Get(L[id], tl, mid, l, r, ans);
Get(R[id], mid, tr, l, r, ans);
}
int n, m, root;
int seg2[SEGSZ2], L2[SEGSZ2], R2[SEGSZ2], ts2;
int Set2(int id, int tl, int tr, int x, int y, ll val){
if (!id) id=++ts2;
if (tr-tl==1) {
seg2[id]=Set(seg2[id], 0, m, y, val);
return id;
}
int mid=(tl+tr)>>1;
if (x<mid) L2[id]=Set2(L2[id], tl, mid, x, y, val);
else R2[id]=Set2(R2[id], mid, tr, x, y, val);
ll res=0;
Get(seg2[L2[id]], 0, m, y, y+1, res);
Get(seg2[R2[id]], 0, m, y, y+1, res);
// debug(res)
seg2[id]=Set(seg2[id], 0, m, y, res);
return id;
}
void Get2(int id, int tl, int tr, int l1, int l2, int r1, int r2){
if (r1<=tl || tr<=l1 || !id) return ;
if (l1<=tl && tr<=r1){
// debug2(tl, tr)
Get(seg2[id], 0, m, l2, r2, ans);
return ;
}
int mid=(tl+tr)>>1;
Get2(L2[id], tl, mid, l1, l2, r1, r2);
Get2(R2[id], mid, tr, l1, l2, r1, r2);
}
void init(int nn, int mm) {
n=nn;
m=mm;
}
void update(int P, int Q, ll K) {
root=Set2(root, 0, n, P, Q, K);
}
ll calculate(int P, int Q, int U, int V) {
ans=0;
Get2(root, 0, n, P, Q, U+1, V+1);
return ans;
}
