#include "game.h"
#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
ll gcd(ll x, ll y) { return !y ? x : gcd(y, x % y); }
int rnd() { return ((rand() % (1 << 15)) << 16) + (rand() % (1 << 15)); }
struct TreapNode {
TreapNode *l, *r;
int pos, key, mn, mx;
ll val, g;
TreapNode(int position, ll value) {
l = r = nullptr;
mn = mx = pos = position;
key = rnd();
val = g = value;
}
void update() {
g = val;
if (l) g = gcd(g, l->g);
if (r) g = gcd(g, r->g);
mn = (l ? l->mn : pos);
mx = (r ? r->mx : pos);
}
};
struct Treap {
TreapNode *root;
Treap() {
root = nullptr;
srand(rnd());
}
void split(TreapNode *t, int pos, TreapNode *&l, TreapNode *&r) {
if (t == nullptr) {
l = r = nullptr;
return;
}
if (t->pos < pos) {
split(t->r, pos, l, r);
t->r = l;
l = t;
} else {
split(t->l, pos, l, r);
t->l = r;
r = t;
}
t->update();
}
TreapNode *merge(TreapNode *l, TreapNode *r) {
if (!l || !r) return l ? l : r;
if (l->key < r->key) {
l->r = merge(l->r, r);
l->update();
return l;
} else {
r->l = merge(l, r->l);
r->update();
return r;
}
}
bool find(int pos) {
TreapNode *t = root;
while (t) {
if (t->pos == pos) return true;
if (t->pos > pos) t = t->l;
else t = t->r;
}
return false;
}
void update(TreapNode *t, int pos, ll val) {
if (t->pos == pos) {
t->val = val;
t->update();
return;
}
if (t->pos > pos) update(t->l, pos, val);
else update(t->r, pos, val);
t->update();
}
void insert(int pos, ll val) {
if (find(pos)) update(root, pos, val);
else {
TreapNode *l, *r;
split(root, pos, l, r);
root = merge(merge(l, new TreapNode(pos, val)), r);
}
}
ll query(TreapNode *t, int st, int en) {
if (t->mx < st || en < t->mn) return 0;
if (st <= t->mn && t->mx <= en) return t->g;
ll ans = (st <= t->pos && t->pos <= en ? t->val : 0);
if (t->l) ans = gcd(ans, query(t->l, st, en));
if (t->r) ans = gcd(ans, query(t->r, st, en));
return ans;
}
ll query(int st, int en) {
if (!root) return 0;
return query(root, st, en);
}
};
struct Segtree {
Segtree *l, *r;
Treap treap;
int lo, hi;
Segtree() { l = r = nullptr; }
Segtree(int st, int en) {
l = r = nullptr;
lo = st, hi = en;
}
void new_left() {
if (!l) l = new Segtree(lo, (lo + hi) / 2);
}
void new_right() {
if (!r) r = new Segtree((lo + hi) / 2 + 1, hi);
}
void fix(int pos) {
ll val = 0;
if (l) val = gcd(val, l->treap.query(pos, pos));
if (r) val = gcd(val, r->treap.query(pos, pos));
treap.insert(pos, val);
}
void update(int x, int y, ll val) {
if (hi < x || x < lo) return;
if (lo == hi) {
treap.insert(y, val);
return;
}
if (x <= (lo + hi) / 2) {
new_left();
l->update(x, y, val);
} else {
new_right();
r->update(x, y, val);
}
fix(y);
}
ll query(int t, int b, int st, int en) {
if (hi < t || b < lo) return 0;
if (t <= lo && hi <= b) return treap.query(st, en);
ll ans = 0;
if (l) ans = gcd(ans, l->query(t, b, st, en));
if (r) ans = gcd(ans, r->query(t, b, st, en));
return ans;
}
};
Segtree segtree;
void init(int R, int C) {
srand(12341234);
segtree = Segtree(0, R - 1);
}
void update(int P, int Q, ll K) { segtree.update(P, Q, K); }
ll calculate(int P, int Q, int U, int V) { return segtree.query(P, U, Q, V); }
