#include "game.h"
#include<bits/stdc++.h>
using namespace std;
const int maxn = 2048;
typedef long long ll;
int n, m;
long long a[maxn][maxn];
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 segtree2d{
struct segtree{
struct Node{
//Node *l, *r;
int l, r;
long long key;
Node(){
key = 0;
l = -1;
r = -1;
}
Node(long long _key){
key = _key;
l = -1;
r = -1;
}
};
vector<Node> t;
//Node *root;
//int root; it is always 0
//segtree *ltree, *rtree;
//long long key;
int ltree, rtree;
segtree(){
ltree = -1;
rtree = -1;
t.emplace_back();
//key = 0;
}
inline void compute(int i){
assert(i != -1);
long long gcdl = (t[i].l == -1)? (long long) 0: t[t[i].l].key;
long long gcdr = (t[i].r == -1)? (long long) 0: t[t[i].r].key;
t[i].key = gcd2(gcdl, gcdr);
/*if (!t->l) t->l = new Node();
if (!t->r) t->r = new Node();
t->key = gcd2(t->l->key, t->r->key);*/
}
void update(int i, int l, int r, int pos, long long value){
assert(i != -1);
//cerr << "update: " << t << " " << l << " " << r << " " << pos << " " << value << "\n";
if (l == r){
t[i].key = value;
return;
}
int mid = (r - l) / 2 + l;
if (pos <= mid){
if (t[i].l == -1){
t[i].l = t.size();
t.emplace_back();
}
update(t[i].l, l, mid, pos, value);
}
else{
if (t[i].r == -1){
t[i].r = t.size();
t.emplace_back();
}
update(t[i].r, mid + 1, r, pos, value);
}
compute(i);
}
inline void Update(int pos, long long value){
update(0, 0, m - 1, pos, value);
}
long long query(int i, int l, int r, int ql, int qr){
assert(i != -1);
if (t[i].key == 0) return (long long) 0;
if (l == ql && r == qr) return t[i].key;
int mid = (r - l) / 2 + l;
if (qr <= mid){
if (t[i].l == -1) return (long long) 0;
//t->l = new Node();
return query(t[i].l, l, mid, ql, qr);
}
if (ql > mid){
if (t[i].r == -1) return (long long) 0;
//t->r = new Node();
return query(t[i].r, mid + 1, r, ql, qr);
}
long long gcdl, gcdr;
/*if (!t->l) t->l = new Node();
if (!t->r) t->r = new Node();*/
gcdl = (t[i].l == -1)? (long long) 0: query(t[i].l, l, mid, ql, mid);
gcdr = (t[i].r == -1)? (long long) 0: query(t[i].r, mid + 1, r, mid + 1, qr);
return gcd2(gcdl, gcdr);
}
long long Query(int ql, int qr){
return query(0, 0, m - 1, ql, qr);
}
};
vector<segtree> t;
//segtree *root;
segtree2d(){
//root = new segtree();
t.emplace_back();
}
inline void compute(int i, int posc){
assert(i != -1);
/*if (!t->ltree) t->ltree = new segtree();
if (!t->rtree) t->rtree = new segtree();*/
//t->key = gcd2(t->ltree->key, t->rtree->key);
long long lgcd = (t[i].ltree == -1)? (long long) 0: t[t[i].ltree].Query(posc, posc);
long long rgcd = (t[i].rtree == -1)? (long long) 0: t[t[i].rtree].Query(posc, posc);
long long value = gcd2(lgcd, rgcd);
t[i].Update(posc, value);
}
void update(int i, int l, int r, int posr, int posc, long long value){
//cerr << "Update row tree: " << t << " " << l << " " << r << " " << posr << " " << posc << " " << value << "\n";
assert(i != -1);
if (l == r){
//cerr << "l == r is true. update locally\n";
t[i].Update(posc, value);
//cerr << "local update is done\n";
return;
}
int mid = (r - l) / 2 + l;
if (posr <= mid){
if (t[i].ltree == -1){
t[i].ltree = t.size();
t.emplace_back();
}
update(t[i].ltree, l, mid, posr, posc, value);
}
else{
if (t[i].rtree == -1){
t[i].rtree = t.size();
t.emplace_back();
}
update(t[i].rtree, mid + 1, r, posr, posc, value);
}
compute(i, posc);
}
void Update(int posr, int posc, long long value){
update(0, 0, n - 1, posr, posc, value);
}
long long query(int i, int l, int r, int qlr, int qrr, int qlc, int qrc){
assert(i != -1);
if (l == qlr && r == qrr){
return t[i].Query(qlc, qrc);
}
int mid = (r - l) / 2 + l;
if (qrr <= mid){
if (t[i].ltree == -1) return (long long) 0;
//t->ltree = new segtree();
return query(t[i].ltree, l, mid, qlr, qrr, qlc, qrc);
}
if (qlr > mid){
if (t[i].rtree == -1) return (long long) 0;
//t->rtree = new segtree();
return query(t[i].rtree, mid + 1, r, qlr, qrr, qlc, qrc);
}
/*if (!t->ltree) t->ltree = new segtree();
if (!t->rtree) t->rtree = new segtree();*/
long long gcdl = (t[i].ltree == -1)? (long long) 0: query(t[i].ltree, l, mid, qlr, mid, qlc, qrc);
long long gcdr = (t[i].rtree == -1)? (long long) 0: query(t[i].rtree, mid + 1, r, mid + 1, qrr, qlc, qrc);
return gcd2(gcdl, gcdr);
}
long long Query(int qlr, int qrr, int qlc, int qrc){
return query(0, 0, n - 1, qlr, qrr, qlc, qrc);
}
};
segtree2d matrix;
void init(int R, int C) {
//cerr << "init\n";
n = R;
m = C;
}
void update(int P, int Q, long long K) {
//a[P][Q] = K;
//cerr << "Update P Q K\n ";
matrix.Update(P, Q, K);
//cerr << "End Update P Q K\n";
}
long long calculate(int P, int Q, int U, int V) {
/*long long gcd = 0;
for (int i = P; i <= U; ++i)
for (int j = Q; j <= V; ++j)
gcd = gcd2(gcd, a[i][j]);*/
//cerr << "Calculate P Q U V\n";
long long gcd = matrix.Query(P, U, Q, V);
//cerr << "End Calculate P Q U V\n";
return gcd;
}
