#include "game.h"
#include<bits/stdc++.h>
using namespace std;
#define mp make_pair
#define INF 10000000
#define MOD 1000000007
#define MID ((l+r)/2)
#define HASHMOD 2305843009213693951
#define ll long long
#define ull unsigned long long
#define F first
#define S second
typedef pair<ll, ll> ii;
typedef pair<ii, int> iii;
typedef vector<ll> vi;
typedef vector<ii> vii;
typedef map<int, int> mii;
#define EPS 1e-6
#define FOR(i,n) for(int i=0;i<((int)(n));i++)
#define FORi(i,a,b) for(int i=((int)(a));i<((int)(b));i++)
#define FOA(v, a) for(auto v : a)
int t, n;
vi a, b;
static int M;
//static map<int, map<ii, int> > mapper;
long long gcd(long long X, long long Y) {
//return X + Y;
long long tmp;
while (X != Y && Y != 0) {
tmp = X;
X = Y;
Y = tmp % Y;
}
return X;
}
template<typename Q>
struct seg_tree_2d{
template<typename T>
struct seg_tree{
struct node{
T val;
int left=-1;
int right=-1;
node() {val=0, left=-1, right=-1;}
node(T v) {val=v, right=-1, left=-1;}
};
int parent;
vector<node> seg;
T RAND_VALUE=0;
seg_tree(){seg.assign(1, node());}
unordered_map<int, T> leaves;
inline node merge(node& par, node& a, node& b){
node ret;
ret.left = par.left, ret.right = par.right;
ret.val = gcd(a.val , b.val);
return ret;
}
inline void update_node(int ind, T val, int l, int r){
//cout<<"Node "<<parent<<" "<<ind<<" "<<l<<" "<<r<<" "<<val<<endl;
//seg[ind].val = 1-seg[ind].val;
leaves[l] = val;
if(val==0) leaves.erase(l);
seg[ind].val = val;
}
inline void create_children(int ind, int l, int r){
if(seg[ind].left==-1) seg[ind].left=seg.size(), /*mapper[parent][{l,MID}] = seg[ind].left,*/ seg.push_back(node());
if(seg[ind].right==-1) seg[ind].right=seg.size(), /*mapper[parent][{MID+1,r}] = seg[ind].right,*/ seg.push_back(node());
}
void print(int l=0, int r=M-1, int ind=0){
cout<<"("<<l<<" "<<r<<" "<<ind<<": "<<seg[ind].val<<") ";
if(seg[ind].left!=-1) print(l, MID, seg[ind].left);
if(seg[ind].right!=-1) print(MID+1, r, seg[ind].right);
}
void build(vector<T>& arr, int l=0, int r=M-1, int ind=0){
if(l==r) seg[ind] = node(arr[l]);
else{
create_children(ind, l, r);
build(arr,l,MID,seg[ind].left);
build(arr,MID+1,r,seg[ind].right);
seg[ind] = merge(seg[ind], seg[seg[ind].left], seg[seg[ind].right]);
}
}
void update(int x, T val, int l=0, int r=M-1, int ind=0){
if(x==l && r==x) update_node(ind, val,l,r);
else if(x<l || r<x) return;
else{
create_children(ind, l, r);
update(x,val,l,MID,seg[ind].left);
update(x,val,MID+1,r,seg[ind].right);
seg[ind] = merge(seg[ind], seg[seg[ind].left], seg[seg[ind].right]);
}
}
T query(int rl, int rr, int l=0, int r=M-1, int ind=0){
if(rl<=l && r<=rr) return seg[ind].val;
else if(rl>r || l>rr) return RAND_VALUE;
else{
create_children(ind, l, r);
return gcd(query(rl, rr, l, MID, seg[ind].left) , query(rl,rr,MID+1,r,seg[ind].right));
}
}
};
struct node{
seg_tree<Q> val;
int left=-1;
int right=-1;
node() {left=-1, right=-1;}
};
vector<node> seg2d;
static inline int N;
Q RAND_VALUE_2d=0;
seg_tree_2d(int n){N=n, seg2d.assign(1, node()); seg2d[0].val.parent = 0;}
inline void merge(node &par, node &a, node &b, int ind){
/*
cout<<"MERGING "<<par.left<<": ";
a.val.print();
cout<<"\nWITH "<<par.right<<": ";
b.val.print();
cout<<endl;
cout<<"CHANGE ";
FOA(v,changed) cout<<"("<<v.F<<" "<<v.S<<") ";
cout<<endl;
*/
//if(par.val.seg.size()==1 && (a.val.seg.size()+b.val.seg.size()>2)){
par.val.parent = ind;
/*
cout<<"LEAVES A: ";
FOA(v,a.val.leaves) cout<<"("<<v.F<<" "<<v.S<<") ";
cout<<endl;
cout<<"LEAVES B: ";
FOA(v,b.val.leaves) cout<<"("<<v.F<<" "<<v.S<<") ";
cout<<endl;
*/
FOA(v,a.val.leaves){
Q val = v.S;
if(b.val.leaves[v.F]) val = gcd(val, b.val.leaves[v.F]);
if(par.val.leaves[v.F]!=val) par.val.update(v.F, val);
}
FOA(v,b.val.leaves){
Q val = v.S;
if(a.val.leaves[v.F]) val = gcd(val, a.val.leaves[v.F]);
if(par.val.leaves[v.F]!=val) par.val.update(v.F, val);
}
//cout<<"LEAVES BOTH: "; FOA(v,leaves_a) cout<<"("<<v.F<<" "<<v.S<<") "; cout<<endl;
/*}
else{
//assert(a.val.parent==seg2d[ind].left);
FOA(v,changed){
cout<<v.F<<" "<<v.S<<endl;
par.val.seg[mapper[ind][v]].val = gcd(a.val.seg[mapper[seg2d[ind].left][v]].val , b.val.seg[mapper[seg2d[ind].right][v]].val);
}
}
*/
//cout<<"RESULT OF MERGE ";
//par.val.print();
//cout<<endl;
}
void print(int l=0, int r=N-1, int ind=0){
cout<<"L R "<<l<<" "<<r<<" "<<ind<<endl;
seg2d[ind].val.print();
cout<<endl;
if(seg2d[ind].left!=-1) print(l, MID, seg2d[ind].left);
if(seg2d[ind].right!=-1) print(MID+1, r, seg2d[ind].right);
}
inline void create_children(int ind){
if(seg2d[ind].left==-1){
seg2d[ind].left=seg2d.size();
seg2d.push_back(node());
seg2d.back().val.parent = seg2d[ind].left;
//mapper[seg2d[ind].left][{0,M-1}] = 0;
}
if(seg2d[ind].right==-1){
seg2d[ind].right=seg2d.size();
seg2d.push_back(node());
seg2d.back().val.parent = seg2d[ind].right;
//mapper[seg2d[ind].right][{0,M-1}] = 0;
}
//if(seg2d[ind].right==-1) seg2d[ind].right=seg2d.size(), seg2d.push_back(node()), seg2d.back().val.parent = seg2d[ind].right;
}
void build(vector<vector<Q> >& arr, int l=0, int r=N-1, int ind=0){
if(l==r){
seg2d[ind].val.build(arr[l]);
}
else{
create_children(ind);
build(arr,l,MID,seg2d[ind].left);
build(arr,MID+1,r,seg2d[ind].right);
merge(seg2d[ind], seg2d[seg2d[ind].left], seg2d[seg2d[ind].right], ind);
}
}
void update(int y, int x, Q val, int l=0, int r=N-1, int ind=0){
if(y==l && y==r) seg2d[ind].val.update(x, val);
else if(y<l || r<y) return;
else{
create_children(ind);
update(y,x,val,l,MID,seg2d[ind].left);
update(y,x,val,MID+1,r,seg2d[ind].right);
merge(seg2d[ind], seg2d[seg2d[ind].left], seg2d[seg2d[ind].right], ind);
}
}
Q query(int rl, int rr, int xl, int xr, int l=0, int r=N-1, int ind=0){
if(rl<=l && r<=rr) return seg2d[ind].val.query(xl, xr);
else if(rl>r || l>rr) return RAND_VALUE_2d;
else{
create_children(ind);
return gcd(query(rl, rr, xl, xr, l, MID, seg2d[ind].left), query(rl,rr,xl, xr, MID+1,r,seg2d[ind].right));
}
}
};
seg_tree_2d<ll> seg(n);
void init(int R, int C) {
M = R;
seg.N = C;
}
void update(int P, int Q, long long K) {
seg.update(Q,P,K);
//seg.print();
/*
FOR(i,M){
FOR(j,M) seg.query(i,i,j,j);
//FOR(j,M) cout<<setw(1)<<seg.query(i,i,j,j);
//cout<<endl;
}
*/
//cout<<endl;
}
long long calculate(int P, int Q, int U, int V) {
return seg.query(Q,V,P,U);
}
/*
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int q;
cin>>n>>q;
init(n,n);
string s[n];
vector<vector<ll> > a(n, vi(n, 0));
FOR(i,n) cin>>s[i];
FOR(i,n) FOR(j,n){
if(s[i][j]=='*') a[i][j] = 1;
else a[i][j] = 0;
}
seg.build(a);
while(q--){
cin>>t;
if(t==1){
int x, y;
cin>>x>>y;
update(x-1,y-1, 1);
}
else{
int x1, y1, x2, y2;
cin>>x1>>y1>>x2>>y2;
cout<<seg.query(x1-1,x2-1, y1-1, y2-1)<<"\n";
}
}
}
*/
