#include "game.h"
#include <bits/stdc++.h>
using namespace std;
const int k_Inf = 1e9;
long long gcd2(long long X, long long Y) {
long long tmp;
while (X != Y && Y != 0) {
tmp = X;
X = Y;
Y = tmp % Y;
}
return X;
}
struct SegmentTree{
vector<long long> nodes;
vector<int> left, right;
void get_new_node(){
nodes.push_back(0);
left.push_back(-1);
right.push_back(-1);
}
void build_kids(int idx){
if(left[idx] == -1){
get_new_node();
left[idx] = nodes.size() - 1;
get_new_node();
right[idx] = nodes.size() - 1;
}
}
SegmentTree(){
get_new_node();
}
void clear(){
nodes.clear();
left.clear();
right.clear();
get_new_node();
}
void update(int idx, int l, int r, int s, long long new_val){
if(s < l || r < s) return;
if(l == r){
nodes[idx] = new_val;
return;
}
build_kids(idx);
int mid = (l + r) >> 1;
update(left[idx], l, mid, s, new_val);
update(right[idx], mid + 1, r, s, new_val);
nodes[idx] = gcd2(nodes[left[idx]], nodes[right[idx]]);
}
long long query(int idx, int l, int r, int sl, int sr){
if(sl > r || sr < l) return 0;
if(sl <= l && r <= sr) return nodes[idx];
if(left[idx] == -1)
return 0;
int mid = (l + r) >> 1;
long long lvalue = query(left[idx], l, mid, sl, sr);
long long rvalue = query(right[idx], mid + 1, r, sl, sr);
return gcd2(lvalue, rvalue);
}
friend void merge(SegmentTree &st1, SegmentTree &st2, SegmentTree &ans, int idx1, int idx2, int idx3){
if((idx1 == -1 || st1.left[idx1] == -1) && (idx2 == -1 || st2.left[idx2] == -1)){
if(idx1 == -1) ans.nodes[idx3] = st2.nodes[idx2];
else if(idx2 == -1) ans.nodes[idx3] = st1.nodes[idx1];
else ans.nodes[idx3] = gcd2(st1.nodes[idx1], st2.nodes[idx2]);
return;
}
ans.build_kids(idx3);
if(idx1 == -1 || st1.left[idx1] == -1){
merge(st1, st2, ans, -1, st2.left[idx2], ans.left[idx3]);
merge(st1, st2, ans, -1, st2.right[idx2], ans.right[idx3]);
}
else if(idx2 == -1 || st2.left[idx2] == -1){
merge(st1, st2, ans, st1.left[idx1], -1, ans.left[idx3]);
merge(st1, st2, ans, st1.right[idx1], -1, ans.right[idx3]);
}
else{
merge(st1, st2, ans, st1.left[idx1], st2.left[idx2], ans.left[idx3]);
merge(st1, st2, ans, st1.right[idx1], st2.right[idx2], ans.right[idx3]);
}
ans.nodes[idx3] = gcd2(ans.nodes[ans.left[idx3]], ans.nodes[ans.right[idx3]]);
}
};
struct SegmentTree2D{
vector<SegmentTree*> nodes;
vector<int> left, right;
void get_new_node(){
nodes.push_back(new SegmentTree());
left.push_back(-1);
right.push_back(-1);
}
void build_kids(int idx){
if(left[idx] == -1){
get_new_node();
left[idx] = nodes.size() - 1;
get_new_node();
right[idx] = nodes.size() - 1;
}
}
SegmentTree2D(){
get_new_node();
}
void update(int idx, int l, int r, int x, int y, long long new_val){
if(x < l || r < x) return;
if(l == r){
nodes[idx]->update(0, 0, k_Inf, y, new_val);
return;
}
build_kids(idx);
int mid = (l + r) >> 1;
update(left[idx], l, mid, x, y, new_val);
update(right[idx], mid + 1, r, x, y, new_val);
long long t = gcd2(nodes[left[idx]]->query(0, 0, k_Inf, y, y), nodes[right[idx]]->query(0, 0, k_Inf, y, y));
nodes[idx]->update(0, 0, k_Inf, y, t);
}
long long query(int idx, int l1, int r1, int sl1, int sr1, int sl2, int sr2){
if(sl1 > r1 || sr1 < l1) return 0;
if(sl1 <= l1 && r1 <= sr1) return nodes[idx]->query(0, 0, k_Inf, sl2, sr2);
if(left[idx] == -1)
return 0;
int mid = (l1 + r1) >> 1;
long long lvalue = query(left[idx], l1, mid, sl1, sr1, sl2, sr2);
long long rvalue = query(right[idx], mid + 1, r1, sl1, sr1, sl2, sr2);
return gcd2(lvalue, rvalue);
}
};
int r, c;
SegmentTree2D st;
void init(int _r, int _c) {
r = _r, c = _c;
}
void update(int p, int q, long long k) {
st.update(0, 0, k_Inf, p, q, k);
}
long long calculate(int p, int q, int u, int v) {
return st.query(0, 0, k_Inf, p, u, q, v);
}
