#include <bits/stdc++.h>
using namespace std;
using ll=long long;
const int p = 1000000007;
const int pLL = 1000000007LL;
const int MAXN = 500001; // 1-index that shit
const ll MAXP = 1000000000;
int n;
int X[MAXN];
int Y[MAXN];
ll x_prod=1;
int gcd(int a, int b, int &x, int &y)
{
if(a%b == 1) // uh ... plug a = p in the real thing I guess then
{
x = 1;
y = -int(a/b);
return 1;
}
int d = gcd(b,a%b,x,y);
int old_x = x;
x = y;
y = old_x - int(a/b)*y;
return d;
}
int mod_inv(int x)
{
if(x==1) return 1; // thonking
int x1=-1;
int y1=-1;
gcd(p,x,x1,y1); // EDITING THIS DAMN FUNCTION !!!
while(y1<0) y1+=p;
return y1;
}
pair<ll,ll> mexico(pair<ll,ll> a, pair<ll,ll> b)
{
if(b.second > MAXP) return a;
if(a.first*b.second >= a.second*b.first) return a;
return b;
}
int init(int N, int x[], int y[])
{
n=N;
for(int i=0; i<n; i++)
{
X[i+1]=x[i];
x_prod *= ll(x[i]);
x_prod %= pLL;
}
for(int i=0; i<n; i++)
{
Y[i+1]=y[i];
}
pair<ll,ll> GL = {ll(Y[n]),1}; // gain and loss
ll cur_loss = 1;
int i = n-1;
while(i>0 && cur_loss <= MAXP)
{
cur_loss *= X[i+1];
GL = mexico(GL, make_pair(ll(Y[i]),cur_loss));
i--;
}
// return x_prod * GL.first * mod_inv(GL.second)
ll ans = x_prod * GL.first;
ans %= pLL;
ans *= ll(mod_inv(int(GL.second)));
ans %= pLL;
return ans;
}
int updateX(int pos, int val)
{
pos++;
x_prod *= ll(mod_inv(X[pos]));
x_prod %= pLL;
x_prod *= val;
x_prod %= pLL;
pair<ll,ll> GL = {ll(Y[n]),1}; // gain and loss
ll cur_loss = 1;
int i = n-1;
while(i>0 && cur_loss <= MAXP)
{
cur_loss *= X[i+1];
GL = mexico(GL, make_pair(ll(Y[i]),cur_loss));
i--;
}
// return x_prod * GL.first * mod_inv(GL.second)
ll ans = x_prod * GL.first;
ans %= pLL;
ans *= ll(mod_inv(int(GL.second)));
ans %= pLL;
return ans;
}
int updateY(int pos, int val)
{
Y[++pos]=val;
pair<ll,ll> GL = {ll(Y[n]),1}; // gain and loss
ll cur_loss = 1;
int i = n-1;
while(i>0 && cur_loss <= MAXP)
{
cur_loss *= X[i+1];
GL = mexico(GL, make_pair(ll(Y[i]),cur_loss));
i--;
}
// return x_prod * GL.first * mod_inv(GL.second)
ll ans = x_prod * GL.first;
ans %= pLL;
ans *= ll(mod_inv(int(GL.second)));
ans %= pLL;
return ans;
}
#ifdef ARTHUR_LOCAL
int X_raw[MAXN-1];
int Y_raw[MAXN-1];
int main()
{
X_raw[0]=2;
X_raw[1]=1;
X_raw[2]=3;
Y_raw[0]=3;
Y_raw[1]=4;
Y_raw[2]=1;
cout << init(3,X_raw,Y_raw) << endl;
cout << updateY(1,2) << endl;
}
#endif
