#include <bits/stdc++.h>
#include "game.h"
#define ll long long
#define ld long double
#define pb push_back
#define fi first
#define se second
#define en '\n'
#define sp ' '
#define tb '\t'
#define ri(n) int n; cin >> n
#define rl(n) ll n; cin >> n
#define rs(s) string s; cin >> s
#define rc(c) char c; cin >> c
#define rv(v) for (auto &x : v) cin >> x
#define pven(v) for (auto x : v) cout << x << en
#define pv(v) for (auto x : v) cout << x << sp; cout << en
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define yes cout << "YES" << en
#define no cout << "NO" << en
#define smin(a, b) a = min(a, b)
#define smax(a, b) a = max(a, b)
#define ssort(a, b) if (a < b) swap(a, b)
#define bitcnt(a) (__builtin_popcountll(a))
#define bithigh(a) (63-__builtin_clzll(a))
#define lg bithigh
#define highpow(a) (1LL << (ll)lg(a))
using namespace std;
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 ll LINF = 4e18;
const int mxN = 1e7+10, mxM = 5e5, INF = 2e9;
ll n, m, node[mxN];
int root2D, N[2], root[mxM], ch[mxN][2], ch2[mxM][2];
int Node(){ return N[0]++; }
int Root(){ root[N[1]] = Node(); return N[1]++; }
int Child(int s, int i){ if (!~s) return -1; if (!~ch[s][i]) ch[s][i] = Node(); return ch[s][i]; }
int _Child(int s, int i){ if (!~s) return -1; return ch[s][i]; }
int Child2(int s, int i){ if (!~s) return -1; if (!~ch2[s][i]) ch2[s][i] = Root(); return ch2[s][i]; }
ll Val(int s){ return (~s ? node[s] : 0); }
void Print(int s, ll l, ll r){
if (!~s) return;
cout << tb << tb << s << sp << l << sp << r << sp << node[s] << en;
ll m = (l + r)>>1;
Print(ch[s][0], l, m);
Print(ch[s][1], m+1, r);
}
void Print(int s){ cout << tb << "SEGTREE\n"; Print(s, 0, n-1); cout << en; }
void Print2D(int s, ll l, ll r){
if (!~s) return;
cout << tb << l << sp << r << en;
Print(root[s]);
ll m = (l + r)>>1;
Print2D(ch2[s][0], l, m);
Print2D(ch2[s][1], m+1, r);
}
void Print2D(){ cout << "2D SEGTREE\n"; Print2D(root2D, 0, m-1); cout << en; }
void update(int s, ll l, ll r, ll pos, ll x){
if (l == r){ node[s] = x; return; }
ll m = (l + r)>>1;
if (pos <= m) update(Child(s, 0), l, m, pos, x);
else update(Child(s, 1), m+1, r, pos, x);
node[s] = gcd2(Val(ch[s][0]), Val(ch[s][1]));
}
void update(int s, ll pos, ll x){ update(s, 0, n-1, pos, x); }
ll query(int s, ll l, ll r, ll ql, ll qr){
if (l > qr || r < ql || !~s) return 0;
if (l >= ql && r <= qr) return node[s];
ll m = (l + r)>>1;
ll a = query(ch[s][0], l, m, ql, qr);
ll b = query(ch[s][1], m+1, r, ql, qr);
return gcd2(a, b);
}
ll query(int s, ll l, ll r){ return query(s, 0, n-1, l, r); }
void update2D(int s, ll l, ll r, ll pos, array<ll, 2> args){
if (l == r){ update(root[s], args[0], args[1]); return; }
ll m = (l + r)>>1;
if (pos <= m) update2D(Child2(s, 0), l, m, pos, args);
else update2D(Child2(s, 1), m+1, r, pos, args);
ll x = (~ch2[s][0] ? query(root[ch2[s][0]], args[0], args[0]) : 0);
ll y = (~ch2[s][1] ? query(root[ch2[s][1]], args[0], args[0]) : 0);
update(root[s], args[0], gcd2(x, y));
}
void update2D(ll i, ll j, ll x){ update2D(root2D, 0, m-1, j, {i, x}); }
ll query2D(int s, ll l, ll r, ll ql, ll qr, array<ll, 2> args){
if (l > qr || r < ql || !~s) return 0;
if (l >= ql && r <= qr) return query(root[s], args[0], args[1]);
ll m = (l + r)>>1;
ll a = query2D(ch2[s][0], l, m, ql, qr, args);
ll b = query2D(ch2[s][1], m+1, r, ql, qr, args);
return gcd2(a, b);
}
ll query2D(ll i1, ll j1, ll i2, ll j2){ return query2D(root2D, 0, m-1, j1, j2, {i1, i2}); }
void init(int R, int C){
memset(root, -1, sizeof(root));
memset(ch, -1, sizeof(ch));
memset(ch2, -1, sizeof(ch2));
n = highpow(R);
if (bitcnt(R) > 1) n <<= 1;
m = highpow(C);
if (bitcnt(C) > 1) m <<= 1;
root2D = Root();
}
void update(int P, int Q, long long K) {
update2D(P, Q, K);
}
long long calculate(int P, int Q, int U, int V) {
return query2D(P, Q, U, V);
}
