#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef pair<db,db> pd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
constexpr int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0
int fstTrue(function<bool(int)> f, int lo, int hi) {
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
int mid = (lo+hi)/2;
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
template<class T> void remDup(vector<T>& v) {
sort(all(v)); v.erase(unique(all(v)),end(v)); }
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
template<class A> str ts(complex<A> c) {
stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
return "("+ts(p.f)+", "+ts(p.s)+")"; }
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << ts(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif
// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
#include "game.h"
// typedef struct node* pn;
// struct node {
// ll d = 0; pn l,r;
// node() { l = r = NULL; }
// };
const int AA = 12e6;
int aa;
ll d[AA]; int lq[AA], rq[AA];
// typedef struct Node* pN;
// struct Node {
// pn d; pN l,r;
// Node() { d = NULL, l = r = NULL; }
// };
const int BB = 400000;
int bb;
int D[BB], LQ[BB], RQ[BB];
int root = 0;
void init(int R, int C) {
/* ... */
}
void tri(ll& a, ll b) { a = __gcd(a,b); }
void UPD(int Q, ll K, int& cur, int L = 0, int R = 1e9) {
// dbg("UPD",Q,K,L,R);
if (!cur) cur = ++aa;
if (L == R) { d[cur] = K; return; }
int M = (L+R)/2;
if (Q <= M) UPD(Q,K,lq[cur],L,M);
else UPD(Q,K,rq[cur],M+1,R);
d[cur] = 0;
if (lq[cur]) tri(d[cur],d[lq[cur]]);
if (rq[cur]) tri(d[cur],d[rq[cur]]);
}
void pull(int Q, int& cur, int l, int r, int L = 0, int R = 1e9) {
if (!cur) cur = ++aa;
d[cur] = 0;
if (l) tri(d[cur],d[l]);
if (r) tri(d[cur],d[r]);
if (L == R) return;
int M = (L+R)/2;
if (Q <= M) pull(Q,lq[cur],lq[l],lq[r],L,M);
else pull(Q,rq[cur],rq[l],rq[r],M+1,R);
}
void upd(int P, int Q, ll K, int& cur, int L = 0, int R = 1e9) {
if (!cur) cur = ++bb;
if (L == R) return UPD(Q,K,D[cur]);
int M = (L+R)/2;
if (P <= M) upd(P,Q,K,LQ[cur],L,M);
else upd(P,Q,K,RQ[cur],M+1,R);
pull(Q,D[cur],D[LQ[cur]],D[RQ[cur]]);
}
void update(int P, int Q, long long K) {
dbg("UPDATE");
upd(P,Q,K,root); }
ll QUERY(int Q, int V, int cur, int L = 0, int R = 1e9) {
if (!cur || R < Q || V < L) return 0;
if (Q <= L && R <= V) return d[cur];
int M = (L+R)/2;
return __gcd(QUERY(Q,V,lq[cur],L,M),QUERY(Q,V,rq[cur],M+1,R));
}
ll query(int P, int U, int Q, int V, int cur, int L = 0, int R = 1e9) {
if (!cur || R < P || U < L) return 0;
if (P <= L && R <= U) return QUERY(Q,V,D[cur]);
int M = (L+R)/2;
return __gcd(query(P,U,Q,V,LQ[cur],L,M),query(P,U,Q,V,RQ[cur],M+1,R));
}
long long calculate(int P, int Q, int U, int V) {
dbg("QUERY");
return query(P,U,Q,V,root);
}
