#include <bits/stdc++.h>
#include "game.h"
using namespace std;
using LL = long long;
constexpr int LIM = 1 << 30;
mt19937 rng{42};
class ImplicitTreap {
private:
struct treap {
int x, y;
int a, b; // closed interval [a, b]
LL val;
LL gcd;
treap* l = nullptr;
treap* r = nullptr;
treap() {}
treap(int x, LL val) : x(x), y(rng()), a(x), b(x), val(val), gcd(val) {}
~treap() {
if (l) delete l;
if (r) delete r;
}
};
inline void clean(treap* const t) {
if (t) {
t->l = t->r = nullptr;
delete t;
}
}
inline LL gcd(const treap* const t) {
return t ? t->gcd : 0LL;
}
inline void upd(treap* const t) {
// assume t->l and t->r are already updated
if (t) {
t->gcd = __gcd(__gcd(t->val, gcd(t->l)), gcd(t->r));
t->a = t->l ? t->l->a : t->x;
t->b = t->r ? t->r->b : t->x;
}
}
void split(treap* const t, const int x, treap*& l, treap*& r) {
// split t in [-inf, x], [x+1, +inf]
if (!t) {
l = r = nullptr;
} else if (t->x <= x) {
split(t->r, x, t->r, r); l = t;
} else {
split(t->l, x, l, t->l); r = t;
}
upd(l);
upd(r);
}
void merge(treap*& t, treap* l, treap* r) {
if (!l || !r) {
t = l ? l : r;
} else if (l->y > r->y) {
merge(l->r, l->r, r); t = l;
} else {
merge(r->l, l, r->l); t = r;
}
upd(t);
}
void insert(treap*& t, treap* const nw) {
// assume nw->x is not present in t
if (!t) {
t = nw;
} else if (nw->y > t->y) {
split(t, nw->x, nw->l, nw->r);
t = nw;
} else {
insert(nw->x <= t->x ? t->l : t->r, nw);
}
upd(t);
}
void erase(treap*& t, const int x) {
if (!t) return;
if (t->x == x) {
treap* tmp = t;
merge(t, t->l, t->r);
clean(tmp);
} else {
erase(x <= t->x ? t->l : t->r, x);
}
upd(t);
}
LL gcd(treap* const t, const int l, const int r) {
upd(t);
if (!t || r < t->a || t->b < l) return 0LL;
if (l <= t->a && t->b <= r) return t->gcd;
return __gcd(__gcd((l <= t->x && t->x <= r ? t->val : 0LL), gcd(t->l, l, r)), gcd(t->r, l, r));
}
// actual treap
treap* t = nullptr;
public:
ImplicitTreap() {}
~ImplicitTreap() {
delete t;
}
void update(int x, LL val) {
// set v[x] = val
erase(t, x);
insert(t, new treap(x, val));
}
LL query(const int l, const int r) {
// return sum [l, r]
return gcd(t, l, r);
}
};
struct st {
int a, b;
st * l = nullptr;
st * r = nullptr;
ImplicitTreap son;
st() {}
st(int a, int b) : a(a), b(b) {}
~st() {
if (l) delete l;
if (r) delete r;
}
friend void st_update(st * const n, const int p, const int q, const LL k) {
if (p < n->a || n->b < p) return;
if (n->a == n->b) {
n->son.update(q, k);
return;
}
// don't update the son if a != b !
// you can't just overwrite all the values in the same row, like in 1d
int m = (n->a + n->b) / 2;
if (p <= m) {
if (!n->l) n->l = new st(n->a, m);
st_update(n->l, p, q, k);
} else {
if (!n->r) n->r = new st(m+1, n->b);
st_update(n->r, p, q, k);
}
// suppose n->l and n->r are either zero or up to date
// rebuild n->son properly
rebuild(n, p, q);
}
friend void rebuild(st * const n, const int p, const int q) {
LL gl = n->l ? n->l->son.query(q, q) : 0LL;
LL gr = n->r ? n->r->son.query(q, q) : 0LL;
n->son.update(q, __gcd(gl, gr));
}
friend LL st_query(st * n, const int p, const int q, const int u, const int v) {
if (!n || u < n->a || n->b < p) return 0LL;
if (p <= n->a && n->b <= u) return n->son.query(q, v);
return __gcd(st_query(n->l, p, q, u, v), st_query(n->r, p, q, u, v));
}
};
st * root;
void cleanup() {
delete root;
}
void init(int r, int c) {
root = new st(0, r);
assert(atexit(cleanup) == 0);
}
void update(int p, int q, LL k) {
st_update(root, p, q, k);
}
long long calculate(int p, int q, int u, int v) {
return st_query(root, p, q, u, v);
}
