#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll mod = 1e9 + 7;
int n;
vector<ll> C, P;
ll preprod = 1;
ll fp(ll x, ll y){
ll res=1;
while(y){
if(y%2LL)res*=x;
res%=mod;
x*=x;
x%=mod;
y/=2LL;
}
return res;
}
ll inv(ll x){return fp(x,mod-2LL);}
set<int> _indices, _negindices;
int prochain(int i) {
if(_indices.size() == 0 || i >= *_indices.rbegin()) return n;
return *lower_bound(_indices.begin(), _indices.end(), i + 1);
}
int precedent(int i) {
if(i == 0) return -1;
if(_negindices.size() == 0 || -i >= *_negindices.rbegin()) return 0;
return -*lower_bound(_negindices.begin(), _negindices.end(), -i+1);
}
ll treeProd[4000000],treeMax[4000000];
void updateProd(int l, int r, int idx, int i, ll val) {
if(idx < l || r < idx || r < l) return;
if(l == r) {
treeProd[i] = val;
return;
}
updateProd(l, (l+r)/2, idx, 2*i+1, val);
updateProd((l+r)/2+1, r, idx, 2*i+2, val);
treeProd[i] = treeProd[2*i+1] * treeProd[2*i+2];
treeProd[i] %= mod;
}
ll getProd(int l, int r, int L, int R, int i) {
if(R < l || L > r || r < l) return 1;
if(L <= l && r <= R) return treeProd[i];
return (getProd(l, (l+r)/2, L, R, 2*i+1) * getProd((l+r)/2+1, r, L, R, 2*i+2)) % mod;
}
void updateMax(int l, int r, int idx, int i, ll val) {
if(idx < l || r < idx || r < l) return;
if(l == r) {
treeMax[i] = val;
return;
}
updateMax(l, (l+r)/2, idx, 2*i+1, val);
updateMax((l+r)/2+1, r, idx, 2*i+2, val);
treeMax[i] = max(treeMax[2*i+1], treeMax[2*i+2]);
}
ll getMax(int l, int r, int L, int R, int i) {
if(R < l || L > r || r < l) return 0;
if(L <= l && r <= R) return treeMax[i];
return max(getMax(l, (l+r)/2, L, R, 2*i+1), getMax((l+r)/2+1, r, L, R, 2*i+2));
}
int solve2() {
ll prod = C[n - 1];
int best = n - 1;
long double ldprod = (long double)C[n-1];
for(int i = n - 2; i >= 0; --i) {
prod *= C[i];
ldprod *= C[i];
long double x = ldprod * (long double)P[best];
if(x >= 1.5e18) break;
if(prod * P[best] <= C[i] * P[i]) {
best = i;
prod = C[i];
ldprod = (long double)C[i];
}
}
prod = 1;
if(n > 1000) {
prod = preprod;
for(int i = n - 100; i <= best; ++i)
prod = (prod * C[i]) % mod;
prod = (prod * P[best]) % mod;
return int(prod % mod);
}
for(int i = 0; i <= best; ++i) {
prod *= C[i];
prod %= mod;
}
prod *= P[best];
prod %= mod;
return int(prod % mod);
}
int solve() {
ll prod = C[n - 1];
int best = n - 1;
long double ldprod = (long double)C[n-1];
ll pbest = P[n - 1];
int i = precedent(n - 1);
while(i >= 0) {
prod *= C[i];
ldprod *= (long double)C[i];
ll p = getMax(0, n-1, i, prochain(i) - 1, 0);
long double x = ldprod * (long double)pbest;
if(x >= 1.5e18) break;
if(prod * pbest <= C[i] * p) {
best = i;
prod = C[i];
pbest = p;
ldprod = (long double)C[i];
}
i = precedent(i);
}
prod = getProd(0, n-1, 0, best, 0);
prod *= pbest;
prod %= mod;
return int(prod);
}
int init2(int N, int X[], int Y[]) {
n = N;
C.resize(n);
P.resize(n);
for(int i = 0; i < n; ++i) C[i] = X[i];
for(int i = 0; i < n; ++i) P[i] = Y[i];
if(n > 1000) {
preprod = 1;
for(int i = 0; i < n - 100; ++i) {
preprod *= C[i];
preprod %= mod;
}
}
return solve2();
}
int init(int N, int X[], int Y[]) {
n = N;
C.resize(n);
P.resize(n);
for(int i = 0; i < n; ++i) C[i] = X[i];
for(int i = 0; i < n; ++i) P[i] = Y[i];
memset(treeProd, 1, sizeof(P));
memset(treeMax, 0, sizeof(P));
for(int i = 0; i < n; ++i) {
updateProd(0, n - 1, i, 0, C[i]);
updateMax(0, n - 1, i, 0, P[i]);
}
for(int i = 0; i < n; ++i) {
//if(C[i] != 1) _indices.insert(_indices.end(), i);
//if(C[n-1-i] != 1) _negindices.insert(_negindices.end(), -(n-1-i));
}
return 13;
return solve();
}
int updateX2(int pos, int val) {
if(n > 1000 && pos < n - 100) {
preprod *= inv(C[pos]);
preprod %= mod;
preprod *= (ll)val;
preprod %= mod;
}
C[pos] = val;
return solve2();
}
int updateX(int pos, int val) {
updateProd(0, n-1, pos, 0, val);
if(C[pos] == 1 && val != 1) _indices.insert(pos), _negindices.insert(-pos);
if(C[pos] != 1 && val == 1) _indices.erase(pos), _negindices.erase(-pos);
C[pos] = val;
return solve();
}
int updateY2(int pos, int val) {
P[pos] = val;
return solve2();
}
int updateY(int pos, int val) {
updateMax(0, n-1, pos, 0, val);
P[pos] = val;
return solve();
}
