#include "game.h"
#ifndef EVAL
#include "grader.cpp"
#endif
#include <bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define ub upper_bound
#define lb lower_bound
#define ll long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(),x.rend()
#define fastios ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define vll vector<ll>
#define vii vector<int>
#define vpii vector<pii>
#define vpll vector<pll>
#define cnt(a)__builtin_popcount(a)
template<class T> bool umin(T& a, const T& b) {return a > b? a = b, true:false;}
template<class T> bool umax(T& a, const T& b) {return a < b? a = b, true:false;}
ll sx, sy;
vector<vector<ll>> tree;
ll gcd2(ll X, ll Y) {
ll tmp;
while (X != Y && Y != 0){
tmp = X, X = Y, Y = tmp % Y;
}return X;
}
void update_r(ll x, ll y, ll val, ll lx, ll rx, ll ly, ll ry, ll xx, ll yy){
if(ly == ry){
if(lx == rx) tree[xx][yy] = (ll)val;
else tree[xx][yy] = (ll)gcd2(tree[xx*2][yy], tree[xx*2+1][yy]);
}else{
ll m = (ly + ry)>>1;
if(y <= m) update_r(x, y, val, lx, rx, ly, m, xx, yy*2);
else update_r(x, y, val, lx, rx, m+1, ry, xx, yy*2+1);
tree[xx][yy] = (ll)gcd2(tree[xx][yy*2], tree[xx][yy*2+1]);
}
}
void update_c(ll x, ll y, ll val, ll lx, ll rx, ll xx){
if(lx != rx){
ll m = (lx + rx)>>1;
if(x <= m) update_c(x, y, val, lx, m, xx*2);
else update_c(x, y, val, m+1, rx, xx*2+1);
}
update_r(x, y, val, lx, rx, 1, sy, xx, 1);
}
void update(int P, int Q, ll K) { update_c(++P, ++Q, K, 1, sx, 1); }
ll qqy(ll ly, ll ry, ll xx, ll qly, ll qry, ll yy){
if(ly > qry || ry < qly) return 0ll;
if(ly >= qly && ry <= qry) return (ll)tree[xx][yy];
int m = (ly + ry)>>1;
ll res1 = (ll)qqy(ly, m, xx, qly, qry, yy*2);
ll res2 = (ll)qqy(m+1, ry, xx, qly, qry, yy*2+1);
return (ll)gcd2(res1, res2);
}
ll qq(ll lx, ll rx, ll qlx, ll qrx, ll qly, ll qry, ll xx){
if(lx > qrx || rx < qlx) return 0ll;
if(lx >= qlx && rx <= qrx) return (ll)qqy(1, sy, xx, qly, qry, 1);
int m = (lx + rx)>>1;
ll res1 = (ll)qq(lx, m, qlx, qrx, qly, qry, xx*2);
ll res2 = (ll)qq(m+1, rx, qlx, qrx, qly, qry, xx*2+1);
return (ll)gcd2(res1, res2);
}
void init(int R, int C) {
sx = 1, sy = 1;
while(sx < R) sx <<= 1;
while(sy < C) sy <<= 1;
tree.assign(sx*2, vll(sy*2, 0ll));
}
ll calculate(int x, int y, int xx, int yy) {
return qq(1, sx, min(x, xx)+1, max(x, xx)+1, min(y, yy)+1, max(y, yy)+1, 1);
}
