// And you curse yourself for things you never done
#include<bits/stdc++.h>
#include "game.h"
#define F first
#define S second
#define PB push_back
#define sz(s) int((s).size())
#define bit(n,k) (((n)>>(k))&1)
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const int inf = 1e9 + 10;
int N, M;
struct node{
ll g = 0, x = 0;
node *L = 0, *R = 0;
int pos = 0, S = 0, MN, MX;
node(int _pos, ll _g){
pos = _pos, g = _g, x = _g, MN = MX = _pos;
S = 1;
}
void rest(int _pos, ll _g){
pos = _pos, g = _g, x = _g, MN = MX = _pos;
S = 1;
}
ll ask(int _pos){
if(pos == _pos)
return x;
if(_pos < pos)
return (L ? L->ask(_pos) : 0);
else
return (R ? R->ask(_pos) : 0);
}
ll ask(int f, int s){
if(f <= MN && MX < s)
return g;
if(s <= MN || MX < f)
return 0;
ll ans = 0;
if(f <= pos && pos < s)
ans = x;
if(L)
ans = __gcd(ans, L->ask(f, s));
if(R)
ans = __gcd(ans, R->ask(f, s));
return ans;
}
};
void build(node* nw){
nw->S = (nw->L ? nw->L->S : 0) + (nw->R ? nw->R->S : 0) + 1;
nw->g = __gcd(nw->x, __gcd( nw->L ? nw->L->g : 0, nw->R ? nw->R->g : 0 ));
nw->MN = min({nw->pos, nw->L ? nw->L->MN : inf, nw->R ? nw->R->MN : inf});
nw->MX = max({nw->pos, nw->L ? nw->L->MX : -inf, nw->R ? nw->R->MX : -inf});
}
void split(node* nw, int x, node *&L, node *&R){
if(nw == 0){
L = R = 0;
return;
}
if(nw->pos < x){
split(nw->R, x, L, R);
nw->R = L;
build(nw);
L = nw;
}
else{
split(nw->L, x, L, R);
nw->L = R;
build(nw);
R = nw;
}
}
node* merge(node *A, node *B){
if(A == 0)
return B;
if(B == 0)
return A;
if((rand() % (A->S + B->S)) < A->S){
A->R = merge(A->R, B);
build(A);
return A;
}
else{
B->L = merge(A, B->L);
build(B);
return B;
}
assert(0);
}
void _put(node *&nw, int pos, ll x){
node *A, *B, *C;
split(nw, pos, A, B);
split(B, pos+1, B, C);
if(B == 0)
B = new node(pos, x);
else
B->rest(pos, x);
nw = merge(A, merge(B, C));
}
struct node2{
node* g = 0;
node2 *L = 0, *R = 0;
void put(int posx, int posy, ll x, int l = 0, int r = N){
ll num = x;
if(r-l > 1){
int mid = (l+r) >> 1;
if(posx < mid){
if(!L)
L = new node2();
L->put(posx, posy, x, l, mid);
}
else{
if(!R)
R = new node2();
R->put(posx, posy, x, mid, r);
}
num = __gcd(L ? L->g->ask(posy) : 0, R ? R->g->ask(posy) : 0);
}
if(!g)
g = new node(posy, num);
else
_put(g, posy, num);
}
ll ask(int f, int s, int ff, int ss, int l = 0, int r = N){
if(r <= f || s <= l)
return 0;
if(f <= l && r <= s)
return g ? g->ask(ff, ss) : 0;
int mid = (l+r) >> 1;
return __gcd(L ? L->ask(f, s, ff, ss, l, mid) : 0, R ? R->ask(f, s, ff, ss, mid, r) : 0);
}
};
node2* root;
void init(int N, int M){
srand(time(0));
::N = N, ::M = M;
root = new node2();
}
void update(int x, int y, ll w){
root->put(x, y, w);
}
ll calculate(int x, int y, int xx, int yy){
return root->ask(x, ++xx, y, ++yy);
}
