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#include "game.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
#define all(x) x.begin(), x.end()
#define kill(x) return cout << x << endl, 0
#define X first
#define Y second
#define endl '\n'
constexpr int N = 2e3 + 10;
ll gcd2(ll x, ll y) {
if (!x) return y;
if (!y) return x;
ll tmp;
while (x != y && y != 0) {
tmp = x;
x = y;
y = tmp % y;
}
return x;
}
struct Tree {
ll data;
pii A, B;
Tree *ul, *ur, *dl, *dr;
Tree(const pii & _A, const pii & _B) : data(0), A(_A), B(_B) {}
ll push(int x, int y, ll val) {
if (x < A.X || y < A.Y || x >= B.X || y >= B.Y)
return data;
if (A.X + 1 == B.X) {
return data = val;
}
if (ul == nullptr) {
pii mid = {(A.X + B.X) >> 1, (A.Y + B.Y) >> 1};
ul = new Tree({A.X, A.Y}, {mid.X, mid.Y});
ur = new Tree({A.X, mid.Y}, {mid.X, B.Y});
dl = new Tree({mid.X, A.Y}, {B.X, mid.Y});
dr = new Tree({mid.X, mid.Y}, {B.X, B.Y});
}
data = ul->push(x, y, val);
data = gcd2(data, ur->push(x, y, val));
data = gcd2(data, dl->push(x, y, val));
data = gcd2(data, dr->push(x, y, val));
return data;
}
ll query(const pii & C, const pii & D) {
if (data == 0 || D.X <= A.X || D.Y <= A.Y || B.X <= C.X || B.Y <= C.Y)
return 0;
if (C.X <= A.X && C.Y <= A.Y && B.X <= D.X && B.Y <= D.Y)
return data;
ll res = ul->query(C, D);
res = gcd2(res, ur->query(C, D));
res = gcd2(res, dl->query(C, D));
res = gcd2(res, dr->query(C, D));
return res;
}
} *root;
void init(int R, int C) {
int n = 1;
while (n < R || n < C) {
n <<= 1;
}
root = new Tree({0, 0}, {n, n});
}
void update(int P, int Q, ll K) {
root->push(P, Q, K);
}
ll calculate(int P, int Q, int U, int V) {
return root->query({P, Q}, {U + 1, V + 1});
}
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