#include "game.h"
#include <vector>
#include <algorithm>
#include <iostream>
using namespace std;
using ll = long long;
const int INF = 1'000'000'000;
ll gcd2(ll X, ll Y) {
ll tmp;
while (X != Y && Y != 0) {
tmp = X;
X = Y;
Y = tmp % Y;
}
return X;
}
struct col_tree
{
int l;
int r;
ll g = 0;
col_tree* left = NULL;
col_tree* right = NULL;
};
col_tree* insert(col_tree* P, int I, ll V)
{
col_tree* node1 = P;
col_tree* node2 = new col_tree{I, I, V, NULL, NULL};
if(node1->l >= node2->l) swap(node1, node2);
int nl = P->l, nr = P->r;
while(1)
{
if((nl+nr)>>1 >= node2->r)
nr = (nl+nr)>>1;
else if((nl+nr)/2+1 <= node1->l)
nl = (nl+nr)/2+1;
else
break;
}
col_tree* par = new col_tree{nl, nr, gcd2(node1->g, node2->g), node1, node2};
return par;
}
void update(col_tree* T, int I, ll V)
{
if(T->r < I || I < T->l) return;
if(T->l == T->r)
{
T->g = V;
}
else
{
if(I <= (T->l+T->r)/2)
{
if(T->left == NULL) T->left = new col_tree{I, I, V, NULL, NULL};
else if(T->left->l <= I && I <= T->left->r) update(T->left, I, V);
else T->left = insert(T->left, I, V);
// update(T->left, I, V);
}
else
{
if(T->right == NULL) T->right = new col_tree{I, I, V, NULL, NULL};
if(T->right->l <= I && I <= T->right->r) update(T->right, I, V);
else T->right = insert(T->right, I, V);
}
ll lg = (T->left == NULL) ? 0 : T->left->g;
ll rg = (T->right == NULL) ? 0 : T->right->g;
T->g = gcd2(lg, rg);
}
}
ll range_gcd(col_tree* T, int L, int R)
{
if(T == NULL) return 0;
else if(R < T->l || T->r < L) return 0;
else if(L <= T->l && T->r <= R) return T->g;
else return gcd2(range_gcd(T->left, L, R), range_gcd(T->right, L, R));
}
struct row_tree
{
col_tree v{0, INF-1, 0, NULL, NULL};
row_tree* left = NULL;
row_tree* right = NULL;
};
row_tree* new_row_tree()
{
return new row_tree;
}
//ro
void update(row_tree* T, int I, int J, ll V, int l, int r)
{
// cerr << "entering row_tree " << l << ' ' << r << "\n";
if(l == r)
{
update(&T->v, J, V);
}
else
{
if(I <= (l+r)/2)
{
if(T->left == NULL) T->left = new_row_tree();
update(T->left, I, J, V, l, (l+r)/2);
}
else
{
if(T->right == NULL) T->right = new_row_tree();
update(T->right, I, J, V, (l+r)/2+1, r);
}
ll lg = (T->left == NULL) ? 0 : range_gcd(&T->left->v, J, J);
ll rg = (T->right == NULL) ? 0 : range_gcd(&T->right->v, J, J);
update(&T->v, J, gcd2(lg, rg));
}
// cerr << "exiting row_tree " << l << ' ' << r << "\n";
}
void update(row_tree* T, int I, int J, ll V)
{
update(T, I, J, V, 0, INF-1);
}
ll grid_gcd(row_tree* T, int R1, int R2, int C1, int C2, int l, int r)
{
if(T == NULL) return 0;
else if(R2 < l || r < R1) return 0;
else if(R1 <= l && r <= R2) return range_gcd(&T->v, C1, C2);
else return gcd2(grid_gcd(T->left, R1, R2, C1, C2, l, (l+r)/2), grid_gcd(T->right, R1, R2, C1, C2, (l+r)/2+1, r));
}
ll grid_gcd(row_tree* T, int R1, int R2, int C1, int C2)
{
return grid_gcd(T, R1, R2, C1, C2, 0, INF-1);
}
row_tree ST;
void init(int R, int C)
{
;
}
void update(int P, int Q, long long K)
{
update(&ST, P, Q, K);
}
ll calculate(int P, int Q, int U, int V)
{
return grid_gcd(&ST, P, U, Q, V);
}
