#include "game.h"
#include <bits/stdc++.h>
#define x first
#define y second
#define all(v) v.begin(), v.end()
#define chkmin(a, b) a = min(a, b)
#define chkmax(a, b) a = max(a, b)
//#define int ll
using namespace std;
typedef long long ll;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef pair<int, int> pii;
typedef vector<pii> vii;
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;
}
const int infinity = 1e9;
mt19937 rng(time(0));
auto Dist = uniform_int_distribution<int>(0, infinity);
inline int mrand() {
return Dist(rng);
}
struct Node {
int index = 0;
ll val = 0, gcd = 0;
int prio;
Node *l = 0, *r = 0;
Node(int i, ll x): index(i), val(x), gcd(x), prio(mrand()) {}
inline void pull() {
gcd = gcd2(val, gcd2(l ? l->gcd : 0, r ? r->gcd : 0));
}
};
typedef Node* pnode;
void Merge(pnode &t, pnode l, pnode r) {
if (!l || !r) {
t = l ? l : r;
return;
}
if (l->prio > r->prio) {
t = l;
Merge(t->r, l->r, r);
} else {
t = r;
Merge(t->l, l, r->l);
}
t->pull();
}
void Split(pnode t, pnode &l, pnode &r, int ind) { // <= ind
if (!t) {
l = r = t;
return;
}
if (t->index <= ind) {
l = t;
Split(t->r, l->r, r, ind);
} else {
r = t;
Split(t->l, l, r->l, ind);
}
if (l) l->pull();
if (r) r->pull();
}
struct Treap {
pnode t = 0;
void insert(int i, ll x) {
pnode l = 0, r = 0, mid = 0;
Split(t, l, r, i - 1);
Split(r, mid, r, i);
if (mid) delete mid;
Merge(t, l, new Node(i, x));
Merge(t, t, r);
}
ll query(int a, int b) {
pnode l = 0, r = 0, mid = 0;
Split(t, l, r, b - 1);
Split(l, l, mid, a - 1);
ll x = mid ? mid->gcd : 0;
Merge(t, l, mid);
Merge(t, t, r);
return x;
}
};
struct Seg {
int n;
vector<Treap> seg;
vi lp, rp;
Seg () {}
Seg (int m): n(m) {
Add();
}
inline void Add() {
seg.push_back(Treap());
lp.push_back(0);
rp.push_back(0);
}
void update(int i, int j, ll x, int ind, int l, int r) {
if (l + 1 == r) {
seg[ind].insert(j, x);
return;
}
if (i < (l + r) >> 1) {
if (!lp[ind]) {
lp[ind] = seg.size();
Add();
}
update(i, j, x, lp[ind], l, (l + r) >> 1);
} else {
if (!rp[ind]) {
rp[ind] = seg.size();
Add();
}
update(i, j, x, rp[ind], (l + r) >> 1, r);
}
x = gcd2(lp[ind] ? seg[lp[ind]].query(j, j + 1) : 0, rp[ind] ? seg[rp[ind]].query(j, j + 1) : 0);
seg[ind].insert(j, x);
}
inline void update(int i, int j, ll x) {
update(i, j, x, 0, 0, n);
}
ll query(int x1, int y1, int x2, int y2, int ind, int l, int r) {
if (x1 <= l && r <= x2) return seg[ind].query(y1, y2);
if (r <= x1 || x2 <= l) return 0;
return gcd2(lp[ind] ? query(x1, y1, x2, y2, lp[ind], l, (l + r >> 1)) : 0,
rp[ind] ? query(x1, y1, x2, y2, rp[ind], (l + r) >> 1, r) : 0);
}
inline ll query(int x1, int y1, int x2, int y2) {
return query(x1, y1, x2, y2, 0, 0, n);
}
};
int n, m;
Seg seg;
void init(int32_t R, int32_t C) {
n = R, m = C;
seg = Seg(n);
}
void update(int32_t p, int32_t q, long long k) {
seg.update(p, q, k);
}
long long calculate(int32_t p, int32_t q, int32_t u, int32_t v) {
return seg.query(p, q, u + 1, v + 1);
}
