#include <bits/stdc++.h>
#include "game.h"
using namespace std;
inline long long gcd(long long a, long long b) {
if (!a || !b) {
return a ^ b;
} else {
int shift = __builtin_ctz(a | b);
b >>= __builtin_ctz(b);
while (a) {
a >>= __builtin_ctz(a);
if (a < b) {
swap(a, b);
}
a -= b;
}
return b << shift;
}
}
class node {
public:
node* p;
node* l;
node* r;
long long key;
long long self;
long long subtree;
node(long long key, long long self): key(key), self(self) {
p = l = r = NULL;
subtree = self;
}
void pull() {
subtree = self;
if (l != NULL) {
l->p = this;
subtree = gcd(subtree, l->subtree);
}
if (r != NULL) {
r->p = this;
subtree = gcd(subtree, r->subtree);
}
}
};
class seg {
public:
seg* l;
seg* r;
node* v;
seg() {
l = r = NULL;
v = NULL;
}
};
int n, m;
seg* root;
bool is_bst_root(node* v) {
if (v == NULL) {
return false;
}
return (v->p == NULL || (v->p->l != v && v->p->r != v));
}
void rotate(node* v) {
node* u = v->p;
v->p = u->p;
if (v->p != NULL) {
if (v->p->l == u) {
v->p->l = v;
}
if (v->p->r == u) {
v->p->r = v;
}
}
if (v == u->l) {
u->l = v->r;
v->r = u;
} else {
u->r = v->l;
v->l = u;
}
u->pull();
v->pull();
}
void splay(node* v) {
if (v == NULL) {
return;
}
while (!is_bst_root(v)) {
node* u = v->p;
if (!is_bst_root(u)) {
if ((u->l == v) ^ (u->p->l == u)) {
rotate(v);
} else {
rotate(u);
}
}
rotate(v);
}
}
pair<node*, int> find(node* v, const function<int(node*)> &go_to) {
if (v == NULL) {
return {NULL, 0};
}
splay(v);
int dir;
while (true) {
dir = go_to(v);
if (dir == 0) {
break;
}
node* u = (dir == -1 ? v->l : v->r);
if (u == NULL) {
break;
}
v = u;
}
splay(v);
return {v, dir};
}
node* get_rightmost(node* v) {
return find(v, [&](node*) {
return 1;
}).first;
}
pair<node*, node*> split(node* v, const function<bool(node*)> &is_right) {
if (v == NULL) {
return {NULL, NULL};
}
pair<node*, int> p = find(v, [&](node* u) {
return is_right(u) ? -1 : 1;
});
v = p.first;
if (p.second == -1) {
node* u = v->l;
if (u == NULL) {
return {NULL, v};
}
v->l = u->p = NULL;
v->pull();
return {u, v};
} else {
node* u = v->r;
if (u == NULL) {
return {v, NULL};
}
v->r = u->p = NULL;
v->pull();
return {v, u};
}
}
node* merge(node* v, node* u) {
if (v == NULL) {
return u;
}
if (u == NULL) {
return v;
}
v = get_rightmost(v);
splay(u);
v->r = u;
v->pull();
return v;
}
node* modify(node* v, long long key, long long self) {
pair<node*, node*> foo = split(v, [&](node* u) {
return u->key >= key;
});
pair<node*, node*> bar = split(foo.second, [&](node* u) {
return u->key > key;
});
if (bar.first == NULL) {
bar.first = new node(key, self);
} else {
bar.first->self = self;
bar.first->pull();
}
return merge(foo.first, merge(bar.first, bar.second));
}
long long query(node* &v, long long l, long long r) {
pair<node*, node*> foo = split(v, [&](node* u) {
return u->key >= l;
});
pair<node*, node*> bar = split(foo.second, [&](node* u) {
return u->key >= r;
});
long long ans = bar.first == NULL ? 0 : bar.first->subtree;
v = merge(foo.first, merge(bar.first, bar.second));
return ans;
}
void modify(seg* &root, int l, int r, int p, long long key, long long self) {
if (root == NULL) {
root = new seg();
}
root->v = modify(root->v, key, self);
if (l != r) {
int y = (l + r) >> 1;
if (p <= y) {
modify(root->l, l, y, p, key, self);
} else {
modify(root->r, y + 1, r, p, key, self);
}
}
}
long long query(seg* root, int l, int r, int ll, int rr, long long lll, long long rrr) {
if (root == NULL) {
return 0;
}
if (ll <= l && r <= rr) {
return query(root->v, lll, rrr);
} else {
int y = (l + r) >> 1;
if (rr <= y) {
return query(root->l, l, y, ll, rr, lll, rrr);
} else if (ll > y) {
return query(root->r, y + 1, r, ll, rr, lll, rrr);
} else {
return gcd(query(root->l, l, y, ll, rr, lll, rrr), query(root->r, y + 1, r, ll, rr, lll, rrr));
}
}
}
void init(int R, int C) {
n = R;
m = C;
}
void update(int P, int Q, long long K) {
modify(root, 0, n - 1, P, (long long) Q * n + P, K);
}
long long calculate(int P, int Q, int U, int V) {
return query(root, 0, n - 1, P, U, (long long) Q * n, (long long) (V + 1) * n);
}
