/*
otherside technique!!
instead of storing the value of log(x_i) + log(y_i), store log(prefix sum of x_i) + log(y_i)
although the problem now becomes lazy prop, i think its much easier to code it this way
*/
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fastIO cin.tie(0); ios::sync_with_stdio(false)
#define MOD 1000000007
double prefXLog[500005];
double xLog[500005];
double yLog[500005];
ll x[500005];
ll y[500005];
ll prefAns[500005];
ll modpow(ll b, ll e) {
if(e == 0) return 1;
else if(e&1) return (b * modpow(b, e-1))%MOD;
else return modpow((b*b) % MOD, e/2);
}
ll modinv(ll b) {
return modpow(b, MOD-2);
}
struct ST{
double sum;
ll ans;
ST *lt, *rt;
int l, r;
double lz;
ll lz2;
void prop() {
if(lz == 0) return;
sum += lz;
ans = (ans * lz2) % MOD;
if(lt) {
lt->lz += lz;
rt->lz += lz;
lt->lz2 *= lz2;
rt->lz2 *= lz2;
lt->lz2 %= MOD;
rt->lz2 %= MOD;
}
lz = double(0.0);
lz2 = 1;
}
void comb() {
if(lt->sum > rt->sum) {
sum = lt->sum;
ans = lt->ans;
} else {
sum = rt->sum;
ans = rt->ans;
}
}
ST() {
sum = lz = double(0.0);
ans = 0;
lz2 = 1;
l = r = -1;
lt = rt = nullptr;
}
ST(ll bl, ll br) {
l = bl; r = br;
lt = rt = nullptr;
sum = lz = double(0.0);
ans = 0;
lz2 = 1;
if(l == r) {
sum = prefXLog[l] + yLog[l];
ans = prefAns[l];
} else {
ll m = (l+r)>>1;
lt = new ST(l, m);
rt = new ST(m+1, r);
comb();
}
}
ll qry() {
return ans;
}
void updX(ll ql, ll qr, ll v) {
prop();
if(qr < l || r < ql) return;
if(l <= ql && qr <= r) {
// ql is the left position
lz += log10(v) - xLog[ql];
lz2 *= v;
lz2 *= modinv(x[ql]);
lz2 %= MOD;
prop();
return;
}
lt->updX(ql, qr, v);
rt->updX(ql, qr, v);
comb();
};
void updY(ll i, ll v) {
if(i < l || r < i) return;
if(l == r && i == r) {
lz += log10(v) - yLog[i];
lz2 *= v;
lz2 *= modinv(y[i]);
lz2 %= MOD;
prop();
return;
}
lt->updY(i, v);
rt->updY(i, v);
comb();
}
};
ST tree;
ll n;
ll init (int N, int X[], int Y[]){
n = N;
for(int i = 0; i < N; i++) {
x[i] = X[i];
xLog[i] = log10(X[i]);
prefXLog[i] = log10(X[i]);
prefAns[i] = X[i];
if(i) {
prefXLog[i] += prefXLog[i-1];
prefAns[i] = ((prefAns[i] * prefAns[i-1]) % MOD + MOD) % MOD;
}
}
for(int i = 0; i < N; i++) {
y[i] = Y[i];
yLog[i] = log10(Y[i]);
prefAns[i] *= Y[i];
prefAns[i] %= MOD;
prefAns[i] += MOD;
prefAns[i] %= MOD;
}
tree = ST(0, N-1);
return tree.qry();
}
ll updateX (int pos, int val) {
tree.updX(pos, n-1, (ll)val);
x[pos] = val;
xLog[pos] = log10(val);
return tree.qry();
}
ll updateY (int pos, int val) {
tree.updY(pos, (ll)val);
y[pos] = val;
yLog[pos] = log10(val);
return tree.qry();
}
