#include "game.h"
#include <bits/stdc++.h>
#define F first
#define S second
#define PB push_back
#define MP make_pair
#define EB emplace_back
#define V vector
#define ALL(v) (v).begin(), (v).end()
#define debug(x) cerr << "LINE(" << __LINE__ << ") -> " << #x << " is " << (x) << endl
using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
typedef V<int> vi;
const int INF = 1e9 + 7;
long long gcd2(long long X, long long Y) {
long long tmp;
while (X != Y && Y != 0) {
tmp = X;
X = Y;
Y = tmp % Y;
}
return X;
}
int R, C;
struct seg_y {
struct node {
node *l, *r;
ll g; // gcd
int lz_pos;
ll lz_val;
bool islz;
node() {
l = r = nullptr;
g = lz_pos = lz_val = 0;
islz = false;
}
node(int _lz_pos, ll _lz_val) {
l = r = nullptr;
lz_pos = _lz_pos;
g = lz_val = _lz_val;
islz = true;
}
};
node* root;
seg_y() {
root = nullptr;
}
ll g(node* t) {
return t ? t -> g : 0LL;
}
void pull(node* t) {
t -> g = gcd2(g(t -> l), g(t -> r));
}
void upd(node* &t, int y, ll val, int tl = 0, int tr = C) {
if(!t) {
t = new node(y, val);
return;
}
int tm = (tl + tr) / 2;
if(t -> islz) {
if(t -> lz_pos == y) {
t -> g = t -> lz_val = val;
return;
}
if(t -> lz_pos < tm) t -> l = new node(t -> lz_pos, t -> lz_val);
else t -> r = new node(t -> lz_pos, t -> lz_val);
t -> islz = false;
}
if(y < tm) upd(t -> l, y, val, tl, tm);
else upd(t -> r, y, val, tm, tr);
pull(t);
}
ll qry(node* t, int l, int r, int tl = 0, int tr = C) {
if(!t) return 0;
if(t -> islz) {
if(l <= t -> lz_pos && t -> lz_pos < r) return t -> lz_val;
else return 0;
}
if(l <= tl && tr <= r) return t -> g;
int tm = (tl + tr) / 2;
ll g = 0;
if(l < tm) g = gcd2(g, qry(t -> l, l, r, tl, tm));
if(r > tm) g = gcd2(g, qry(t -> r, l, r, tm, tr));
return g;
}
void upd(int y, ll val) {
upd(root, y, val);
}
ll qry(int l, int r) {
return qry(root, l, r);
}
ll qry(int y) {
return qry(y, y + 1);
}
};
struct seg_x {
struct node {
node *l, *r;
seg_y seg;
node() {
l = r = nullptr;
}
};
node* root;
void pull(node* t, int y) {
ll g = 0;
if(t -> l) g = gcd2(g, t -> l -> seg.qry(y));
if(t -> r) g = gcd2(g, t -> r -> seg.qry(y));
t -> seg.upd(y, g);
}
void upd(node* &t, int x, int y, ll val, int tl = 0, int tr = R) {
if(!t) t = new node();
if(tr - tl == 1) {
t -> seg.upd(y, val);
return;
}
int tm = (tl + tr) / 2;
if(x < tm) upd(t -> l, x, y, val, tl, tm);
else upd(t -> r, x, y, val, tm, tr);
pull(t, y);
}
void upd(int x, int y, ll val) {
upd(root, x, y, val);
}
ll qry(node* t, int xl, int xr, int yl, int yr, int tl = 0, int tr = R) {
if(!t) return 0;
if(xl <= tl && tr <= xr) return t -> seg.qry(yl, yr);
int tm = (tl + tr) / 2;
ll g = 0;
if(xl < tm) g = gcd2(g, qry(t -> l, xl, xr, yl, yr, tl, tm));
if(xr > tm) g = gcd2(g, qry(t -> r, xl, xr, yl, yr, tm, tr));
return g;
}
ll qry(int xl, int xr, int yl, int yr) {
return qry(root, xl, xr, yl, yr);
}
} seg;
void init(int R, int C) {
::R = R, ::C = C;
}
void update(int P, int Q, long long K) {
seg.upd(P, Q, K);
}
long long calculate(int P, int Q, int U, int V) {
return seg.qry(P, U + 1, Q, V + 1);
}
