/**
* author: wxhtzdy
* created: 10.07.2022 09:47:45
**/
// learning 2d segment tree of treaps from USACO Guide
#include "game.h"
#include <bits/stdc++.h>
using namespace std;
mt19937 rng(time(0));
struct TreapNode {
TreapNode *l, *r;
int pos, key, mn, mx;
long long val, g;
TreapNode(int position, long long value) {
l = r = nullptr;
mn = mx = pos = position;
key = rng();
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;
}
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;
}
}
TreapNode* merge(TreapNode *l, TreapNode *r) {
if (!l) return r;
if (!r) return l;
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, long long value) {
if (t->pos == pos) {
t->val = value;
t->update();
return;
}
if (t->pos > pos) {
update(t->l, pos, value);
} else {
update(t->r, pos, value);
}
t->update();
}
void insert(int pos, long long value) {
if (find(pos)) {
update(root, pos, value);
return;
}
TreapNode *l, *r;
split(root, pos, l, r);
root = merge(merge(l, new TreapNode(pos, value)), r);
}
long long query(TreapNode *t, int l, int r) {
if (t->mx < l || t->mn > r) return 0LL;
if (l <= t->mn && t->mx <= r) return t->g;
long long res = 0;
if (l <= t->pos && t->pos <= r) {
res = t->val;
}
if (t->l) res = __gcd(res, query(t->l, l, r));
if (t->r) res = __gcd(res, query(t->r, l, r));
return res;
}
long long query(int l, int r) {
if (!root) return 0LL;
return query(root, l, r);
}
};
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) {
long long 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, long long val) {
if (hi < x || lo > x) return;
if (lo == hi) {
treap.insert(y, val);
return;
}
int mid = (lo + hi) / 2;
if (x <= mid) {
new_left();
l->update(x, y, val);
} else {
new_right();
r->update(x, y, val);
}
fix(y);
}
long long query(int t, int b, int st, int en) {
if (hi < t || lo > b) return 0LL;
if (t <= lo && hi <= b) return treap.query(st, en);
long long 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) {
segtree = Segtree(0, R - 1);
}
void update(int P, int Q, long long K) {
segtree.update(P, Q, K);
}
long long calculate(int P, int Q, int U, int V) {
return segtree.query(P, U, Q, V);
}
