#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
inline 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_N = 1000000001;
struct Treap {
int p;
long long key, key_min, key_max;
long long val, seg;
Treap *ch[2];
Treap(long long k, long long v) : p(mt_rand()), key(k), key_min(k), key_max(k), val(v), seg(v) {
ch[0] = ch[1] = NULL;
}
Treap() {}
};
// inline long long seg(Treap *t) { return t ? t->seg : 0; }
inline Treap *update(Treap *t) {
if (t == NULL) return t;
t->seg = t->val;
t->key_min = t->key;
t->key_max = t->key;
rep(c, 2) if (t->ch[c]) {
t->seg = gcd(t->seg, t->ch[c]->seg);
t->key_min = min(t->key_min, t->ch[c]->key_min);
t->key_max = max(t->key_max, t->ch[c]->key_max);
}
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 };
}
}
vector<long long> gcd_bucket;
void range_seg(Treap *t, long long a, long long b) {
if (t == NULL) return;
long long l = t->key_min, r = t->key_max+1;
if (b <= l || r <= a) return;
if (a <= l && r <= b) {
gcd_bucket.pb(t->seg);
return;
}
if (a <= t->key && t->key < b) gcd_bucket.pb(t->val);
range_seg(t->ch[0], a, b);
range_seg(t->ch[1], a, b);
}
void print(Treap *t) {
if (t == NULL) return;
print(t->ch[0]);
cout << t->key<<"->"<<t->val<<"\n";
print(t->ch[1]);
}
int V = 0;
Treap pool[700000];
inline Treap *alloc(long long key, long long val) {
return &(pool[V++] = Treap(key, val));
}
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);
if (s2._1 == NULL) s2._1 = alloc(key, val);
else s2._1->val = s2._1->seg = val;
treap = merge(s._1, merge(s2._1, s2._2));
}
void gcd(long long l, long long r) { range_seg(treap, l, r); }
};
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_N) {
mp.update(1LL*MAX_N*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);
}
}
void query(int a, int b, int ql, int qr, int l=0, int r=MAX_N) {
if (b <= l || r <= a) return;
if (a <= l && r <= b) return mp.gcd(1LL*MAX_N*ql, 1LL*MAX_N*qr);
if (lch) lch->query(a, b, ql, qr, l, (l+r)/2);
if (rch) rch->query(a, b, ql, qr, (l+r)/2, r);
}
};
SegTree root;
void init(int R, int C) {}
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) {
root.query(P, U+1, Q, V+1);
long long g = 0;
for (long long x : gcd_bucket) g = gcd(g, x);
gcd_bucket.clear();
return g;
}
