#include "horses.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<int> 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)
template<typename T>
struct seg_tree{
struct node{
T val;
T laz;
int left=-1;
int right=-1;
node() {val=0, laz=0, left=-1, right=-1;}
node(T v) {val=v, laz=0, right=-1, left=-1;}
};
vector<node> seg;
static inline int N;
const int RAND_VALUE=0;
seg_tree(int n){N=n, seg.assign(1, node());}
inline node merge(node par, node a, node b){
node ret;
ret.left = par.left, ret.right = par.right;
ret.val = a.val + b.val;
return ret;
}
inline void update_node(int ind, int val, int l, int r){
seg[ind].val = val * (r-l+1);
seg[ind].laz = val;
}
inline void down(node &par, int l, int r){
if(par.laz){
seg[par.left].val += par.laz * (MID-l+1);
seg[par.right].val += par.laz * (r-MID);
seg[par.left].laz = par.laz;
seg[par.right].laz = par.laz;
}
par.laz = 0;
}
inline void create_children(int ind){
node par = seg[ind];
if(par.left==-1) par.left=seg.size(), seg.push_back(node());
if(par.right==-1) par.right=seg.size(), seg.push_back(node());
seg[ind] = par;
}
void build(vector<T>& arr, int l=0, int r=N-1, int ind=0){
if(l==r) seg[ind] = node(arr[l]);
else{
create_children(ind);
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 rl, int rr, int val, int l=0, int r=N-1, int ind=0){
if(rl<=l && r<=rr) update_node(ind, val,l,r);
else if(rr<l || r<rl) return;
else{
create_children(ind);
down(seg[ind],l,r);
update(rl,rr,val,l,MID,seg[ind].left);
update(rl,rr,val,MID+1,r,seg[ind].right);
seg[ind] = merge(seg[ind], seg[seg[ind].left], seg[seg[ind].right]);
}
}
node _query(int rl, int rr, int l=0, int r=N-1, int ind=0){
if(rl<=l && r<=rr) return seg[ind];
else if(rl>r || l>rr) return RAND_VALUE;
else{
create_children(ind);
down(seg[ind],l,r);
return merge(seg[ind], _query(rl, rr, l, MID, seg[ind].left), _query(rl,rr,MID+1,r,seg[ind].right));
}
}
T query(int l, int r){
return _query(l,r).val;
}
};
vi x, y;
int n;
int init(int N, int X[], int Y[]) {
n = N;
x.resize(n);
y.resize(n);
FOR(i,n) x[i] = X[i], y[i] = Y[i];
ll d = 1;
int ppos=0;
FORi(i,1,n){
d*=x[i];
if(y[ppos]/y[i]<d) ppos = i, d=1;
}
ll ans = 1;
FOR(i,ppos+1){
ans = (ans*x[i])%MOD;
}
ans = (ans*y[ppos])%MOD;
return ans;
}
int updateX(int pos, int val) {
x[pos] = val;
ll d = 1;
int ppos=0;
FORi(i,1,n){
d*=x[i];
if(y[ppos]/y[i]<d) ppos = i, d=1;
}
ll ans = 1;
FOR(i,ppos+1){
ans = (ans*x[i])%MOD;
}
ans = (ans*y[ppos])%MOD;
return ans;
}
int updateY(int pos, int val) {
y[pos] = val;
ll d = 1;
int ppos=0;
FORi(i,1,n){
d*=x[i];
if(y[ppos]/y[i]<d) ppos = i, d=1;
}
ll ans = 1;
FOR(i,ppos+1){
ans = (ans*x[i])%MOD;
}
ans = (ans*y[ppos])%MOD;
return ans%MOD;
}
