#include <bits/stdc++.h>
#include "game.h"
using namespace std;
// Pura Gente del Coach Moy y la Alexbriza
using ll = long long;
struct TreapNode {
TreapNode *l = 0, *r = 0;
int i, j, y;
ll val, g;
TreapNode(int i, int j, ll val) : i(i), j(j), y(rand()), val(val), g(val) {}
void recalc();
};
ll getGcd(TreapNode* n) { return n ? n->g : 0; }
void TreapNode::recalc() { g = gcd(val, gcd(getGcd(l), getGcd(r))); }
pair<TreapNode*, TreapNode*> split(TreapNode* n, int i, int j) {
if (!n) return {};
if (make_pair(n->j, n->i) >= make_pair(j, i)) {
auto [L,R] = split(n->l, i, j);
n->l = R;
n->recalc();
return {L, n};
} else {
auto [L,R] = split(n->r, i, j);
n->r = L;
n->recalc();
return {n, R};
}
}
TreapNode* merge(TreapNode* l, TreapNode* r) {
if (!l) return r;
if (!r) return l;
if (l->y > r->y) {
l->r = merge(l->r, r);
return l->recalc(), l;
} else {
r->l = merge(l, r->l);
return r->recalc(), r;
}
}
void setTreap(TreapNode*& n, int i, int j, ll x) {
auto [L1, R1] = split(n, i, j);
auto [L2, R2] = split(R1, i + 1, j);
n = merge(L1, merge(new TreapNode(i, j, x), R2));
}
ll queryTreap(TreapNode* n, int j1, int j2) {
auto [L1, R1] = split(n, 0, j1);
auto [L2, R2] = split(R1, 0, j2);
ll g = getGcd(L2);
n = merge(L1, merge(L2, R2));
return g;
}
struct STree {
struct Node {
TreapNode* treapRoot = nullptr;
int l = -1, r = -1;
};
int n;
vector<Node> st = vector<Node>(1);
STree(int n) : n(n) {}
int set(int v, int tl, int tr, int i, int j, ll val) {
if (v == -1) {
v = int(st.size());
st.emplace_back();
}
setTreap(st[v].treapRoot, i, j, val);
if (tl + 1 == tr) return v;
int tm = (tl + tr) / 2;
i < tm ? st[v].l = set(st[v].l, tl, tm, i, j, val) : st[v].r = set(st[v].r, tm, tr, i, j, val);
return v;
}
ll query(int v, int tl, int tr, int i1, int i2, int j1, int j2) {
if (tr <= i1 || i2 <= tl || v == -1) return 0;
if (i1 <= tl && tr <= i2) return queryTreap(st[v].treapRoot, j1, j2);
int tm = (tl + tr) / 2;
return gcd(query(st[v].l, tl, tm, i1, i2, j1, j2), query(st[v].r, tm, tr, i1, i2, j1, j2));
}
void set(int i, int j, ll val) { set(0, 0, n, i, j, val); }
ll query(int i1, int i2, int j1, int j2) { return query(0, 0, n, i1, i2, j1, j2); }
};
STree st = STree(1000000000);
void init(int R, int C) { }
void update(int P, int Q, ll K) { st.set(P, Q, K); }
ll calculate(int P, int Q, int U, int V) { return st.query(P, U + 1, Q, V + 1); }
