#include<bits/stdc++.h>
#include"horses.h"
using namespace std;
#define ld long double
#define ll long long
const int mod=1e9+7;
vector<int> x,y;
int n ;
set<pair<int,int>,greater<pair<int,int>>> s;
vector<int> seg;
ll prod;
ll exp(int x,int pot){
ll pat=x;
ll ret=1;
while(pot){
if(pot%2){
ret*=pat;
ret%=mod;
}
pat*=pat;
pat%=mod;
pot/=2;
}
return ret;
}
ll inv(int x){
return exp(x,mod-2);
}
void update(int pos, int ini, int fim, int id, int val){
if(ini>id || fim<id)return;
if(ini==fim){
seg[pos]=val;return;
}
int e=2*pos,d=2*pos+1;
int m=(ini+fim)/2;
update(e,ini,m,id,val);
update(d,m+1,fim,id,val);
seg[pos]=max(seg[e],seg[d]);
}
int query(int pos, int ini,int fim, int l, int r){
if(ini>r || fim<l)return 1;
if(l<= ini && fim <= r)return seg[pos];
int m=(ini+fim)/2;
int e=2*pos,d=2*pos+1;
return max(query(e,ini,m,l,r),query(d,m+1,fim,l,r));
}
int calc(){
auto pt=s.begin();
ll prodat=1;
int rx=1;
int ry=1;
ld r=1;
while(pt!=s.end() && prodat<mod){
auto [id,val]=(*pt);
pt++;
int yat=query(1,1,n,id,n);
ld at=(ld)prodat/(ld)yat;
if(at<r){
r=at;
rx=prodat;
ry=yat;
}
prodat*=val;
}
ll resp=prod;
resp*=ry;
resp%=mod;
resp*=inv(rx);
resp%=mod;
return resp;
}
int init(int N, int X[], int Y[]){
n=N;
prod=1;
x.resize(n+1),y.resize(n+1);
s.insert({0,1});
seg.resize(4*n+8);
for(int i=0;i<n;i++){
x[i+1]=X[i];
prod*=x[i+1];
prod%=mod;
y[i+1]=Y[i];
update(1,1,n,i+1,y[i+1]);
if(x[i+1]!=1){
s.insert({i+1,x[i+1]});
}
}
return calc();
}
int updateX(int pos, int val){
pos++;
if(x[pos]!=1){
s.erase({pos,x[pos]});
prod*=inv(x[pos]);
prod%=mod;
}
x[pos]=val;
if(x[pos]!=1){
prod*=x[pos];
prod%=mod;
s.insert({pos,x[pos]});
}
return calc();
}
int updateY(int pos, int val){
pos++;
update(1,1,n,pos,val);
return calc();
}
