#include "game.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
long long gcd2(long long X, long long Y) {
if (!X) return Y;
if (!Y) return X;
return gcd2(Y, X % Y);
}
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
struct Treap {
struct Node {
ll val, g;
ll prior, pos, mn, mx;
Node *left, *right;
Node(ll _pos, ll _val) {
pos = mn = mx = _pos;
val = g = _val;
prior = rng();
left = right = nullptr;
}
void update() {
g = val;
if (left) {g = gcd2(g, left->g);}
if (right) {g = gcd2(g, right->g);}
mn = (left ? left->mn : pos);
mx = (right ? right->mx : pos);
}
};
Node *root;
Treap() : root(nullptr) {}
void split(Node *T, Node *&L, Node *&R, ll sep) {
// splits T into L = [mn..pos] and R = [pos+1..mx]
if (!T) {
L = R = nullptr;
return;
}
if (T->pos <= sep) {
split(T->right, T->right, R, sep);
L = T;
} else {
split(T->left, L, T->left, sep);
R = T;
}
T->update();
}
void merge(Node *&T, Node *L, Node *R) {
// merges L and R into T, assuming that all elements in L < R
if (!L || !R) {
T = (L ? L : R);
return;
}
if (L->prior >= R->prior) {
merge(L->right, L->right, R);
T = L;
} else {
merge(R->left, L, R->left);
T = R;
}
T->update();
}
bool find(ll pos) {
// returns TRUE if the node with position pos is present in the treap
Node *cur = root;
while (cur) {
if (cur->pos == pos) {return true;}
if (cur->pos < pos) {cur = cur->right;}
else {cur = cur->left;}
}
return false;
}
void updateNode(Node *cur, ll pos, ll val) {
// updates node at position pos with val, assuming the node exists
if (cur->pos == pos) {
cur->val = val;
cur->update();
return;
}
if (cur->pos < pos) {
updateNode(cur->right, pos, val);
} else {
updateNode(cur->left, pos, val);
}
cur->update();
}
void update(ll pos, ll val) {
// if the node exists, update it
if (find(pos)) {updateNode(root, pos, val);}
else {
// insert a new node
Node *tmp = new Node(pos, val);
Node *t1, *t2;
split(root, t1, t2, pos);
merge(root, t1, tmp);
merge(root, root, t2);
}
}
ll query(Node *T, ll L, ll R) {
// returns sum of all nodes in the range [L..R] under node T
if (!T) return 0;
if (T->mx < L || R < T->mn) return 0;
if (L <= T->mn && T->mx <= R) {
//cout << "{" << T->mn << ", " << T->mx << ": " << T->g << "} ";
return T->g;
}
ll ret;
if (L <= T->pos && T->pos <= R) {
//cout << "{" << T->pos << ", " << T->pos << ": " << T->val << "} ";
ret = T->val;
} else {
ret = 0;
}
if (T->left) {ret = gcd2(ret, query(T->left, L, R));}
if (T->right) {ret = gcd2(ret, query(T->right, L, R));}
return ret;
}
ll query(ll L, ll R) {
// returns sum of all nodes in the range [L..R]
return query(root, L, R);
}
void print(Node *T) {
if (!T) return;
cout << T->pos << ' ' << T->val << ' ' << T->g << ' ' << T->mn << ' ' << T->mx << '\n';
print(T->left);
print(T->right);
}
void print() {
print(root);
}
};
struct DynamicSegtreeBBST {
struct Node {
Treap inner;
Node* left;
Node* right;
Node() {
inner = Treap();
left = right = nullptr;
}
void update(ll pos) {
ll tmp = 0;
if (left) {tmp = gcd(tmp, left->inner.query(pos, pos));}
if (right) {tmp = gcd(tmp, right->inner.query(pos, pos));}
inner.update(pos, tmp);
}
};
Node* root;
ll dim1, dim2;
DynamicSegtreeBBST(ll _dim1, ll _dim2) {
root = new Node();
dim1 = _dim1, dim2 = _dim2;
}
void update(Node* cur, ll l, ll r, ll d1, ll d2, ll upd) {
if (l == r) {
cur->inner.update(d2, upd);
return;
}
ll m = (l + r) >> 1;
if (d1 <= m) {
if (!cur->left) {cur->left = new Node();}
update(cur->left, l, m, d1, d2, upd);
} else {
if (!cur->right) {cur->right = new Node();}
update(cur->right, m+1, r, d1, d2, upd);
}
cur->update(d2);
}
ll query(Node* cur, ll l, ll r, ll d1l, ll d1r, ll d2l, ll d2r) {
if (l > d1r || d1l > r) {return 0;}
if (d1l <= l && r <= d1r) {
//debug(l); debug(r);
//cur->inner.print();
//cout << "{" << l << ", " << r << "} : ";
ll ret = cur->inner.query(d2l, d2r);
//cout << ": " << ret << '\n';
//debug(ret);
return ret;
}
ll m = (l + r) >> 1, ret = 0;
if (cur->left) {ret = gcd2(ret, query(cur->left, l, m, d1l, d1r, d2l, d2r));}
if (cur->right) {ret = gcd2(ret, query(cur->right, m+1, r, d1l, d1r, d2l, d2r));}
return ret;
}
void print() {
for (ll i = 1; i <= dim1; i++) {
for (ll j = 1; j <= dim2; j++) {
cout << query(root, 1, dim1, i, i, j, j) << ' ';
}
cout << '\n';
}
cout << '\n';
}
};
DynamicSegtreeBBST *D;
int R, C;
void init(int R, int C) {
::R = R;
::C = C;
D = new DynamicSegtreeBBST(R, C);
}
void update(int P, int Q, long long K) {
D->update(D->root, 1, R, P+1, Q+1, K);
//D->print();
}
long long calculate(int P, int Q, int U, int V) {
return D->query(D->root, 1, R, P+1, U+1, Q+1, V+1);
}
