#include "game.h"
#include <iostream>
#include <string>
#include <vector>
#include <cmath>
#include <queue>
#include <set>
#include <cassert>
#include <algorithm>
#include <random>
#include <ctime>
using namespace std;
typedef pair<int, int> P;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(x) x.begin(), x.end()
#define uniq(x) x.erase(unique(all(x)), x.end())
#define pb push_back
#define _1 first
#define _2 second
#define INF 1145141919
#define MOD 1000000007
long long gcd(long long X, long long Y) {
long long tmp;
while (X != Y && Y != 0) {
tmp = X;
X = Y;
Y = tmp % Y;
}
return X;
}
mt19937 mt_rand(time(NULL));
//const int MAX_R = 2000;
//const int MAX_C = 100000;
const int MAX_R = 1000000000;
const int MAX_C = 1000000000;
const int MAX_N2 = MAX_R+1;
const long long MAX_N = 1LL*(MAX_R+1)*(MAX_C+1);
struct Treap {
int p;
long long key, val, seg;
Treap *ch[2];
Treap(long long k, long long v) : p(mt_rand()), key(k), val(v), seg(v) {
ch[0] = ch[1] = NULL;
}
};
inline long long seg(Treap *t) { return t ? t->seg : 0; }
inline Treap *update(Treap *t) {
if (t == NULL) return t;
t->seg = gcd(gcd(seg(t->ch[0]), seg(t->ch[1])), t->val);
return t;
}
Treap *merge(Treap *l, Treap *r) {
if (l == NULL) return r;
if (r == NULL) return l;
if (l->p > r->p) {
l->ch[1] = merge(l->ch[1], r);
return update(l);
}
else {
r->ch[0] = merge(l, r->ch[0]);
return update(r);
}
}
// k=lower_bound(val), [0, k) | [k, n)
pair<Treap*, Treap*> splitByValue(Treap *t, long long val) {
if (t == NULL) return {NULL, NULL};
if (val <= t->key) {
auto s = splitByValue(t->ch[0], val);
t->ch[0] = s._2;
return { s._1, update(t) };
}
else {
auto s = splitByValue(t->ch[1], val);
t->ch[1] = s._1;
return { update(t), s._2 };
}
}
void print(Treap *t) {
if (t == NULL) return;
print(t->ch[0]);
cout << t->key<<"->"<<t->val<<"\n";
print(t->ch[1]);
}
struct TMap {
Treap *treap;
TMap() : treap(NULL) {}
void update(long long key, long long val) {
auto s = splitByValue(treap, key);
auto s2 = splitByValue(s._2, key+1);
Treap *v = new Treap(key, val);
treap = merge(s._1, merge(v, s2._2));
}
long long query(long long l, long long r) {
auto s = splitByValue(treap, l);
auto s2 = splitByValue(s._2, r);
long long ret = seg(s2._1);
treap = merge(s._1, merge(s2._1, s2._2));
return ret;
}
};
struct SegTree {
SegTree *lch, *rch;
TMap mp;
SegTree() : lch(NULL), rch(NULL) {}
void update(int x, int y, long long v, int l=0, int r=MAX_N2) {
mp.update(1LL*MAX_N2*y+x, v);
if (r-l == 1) return;
if (x < (l+r)/2) {
if (lch == NULL) lch = new SegTree();
lch->update(x, y, v, l, (l+r)/2);
}
else {
if (rch == NULL) rch = new SegTree();
rch->update(x, y, v, (l+r)/2, r);
}
}
long long query(int a, int b, int ql, int qr, int l=0, int r=MAX_N2) {
if (b <= l || r <= a) return 0;
if (a <= l && r <= b) return mp.query(1LL*MAX_N2*ql, 1LL*MAX_N2*qr);
return gcd(lch?lch->query(a, b, ql, qr, l, (l+r)/2):0,
rch?rch->query(a, b, ql, qr, (l+r)/2, r):0);
}
};
SegTree root;
void init(int R, int C) {
TMap mp;
}
void update(int P, int Q, long long K) {
root.update(P, Q, K);
}
long long calculate(int P, int Q, int U, int V) {
return root.query(P, U+1, Q, V+1);
}
