#include "horses.h"
#include <bits/stdc++.h>
#define fr first
#define sc second
#define mk make_pair
#define pb push_back
#define all(s) s.begin(), s.end()
using namespace std;
const int N = 5e5 + 5, mod = 1e9 + 7;
int a[N], b[N], n;
long long pr[N];
long double pref[N], eps = 1e-13;
struct asd {
long long val, must;
long double mx, add;
asd() {
must = 1;
}
};
asd t[N * 4];
void build (int v = 1, int tl = 0, int tr = n - 1) {
if (tl == tr) {
t[v].val = pr[tl] * 1ll * b[tl] % mod;
t[v].mx = pref[tl] + log10(b[tl] + eps);
} else {
int tm = (tl + tr) >> 1;
build(v + v, tl, tm);
build(v + v + 1, tm + 1, tr);
if (t[v + v].mx - t[v + v + 1].mx > eps) {
t[v].val = t[v + v].val;
t[v].mx = t[v + v].mx;
} else {
t[v].val = t[v + v + 1].val;
t[v].mx = t[v + v + 1].mx;
}
}
}
int init(int N, int X[], int Y[]) {
n = N;
for (int i = 0; i < n; i++) {
a[i] = X[i]; b[i] = Y[i];
pref[i] = (i == 0 ? 0 : pref[i - 1]) + log10(a[i] + eps);
pr[i] = (i == 0 ? 1 : pr[i - 1]) * 1ll * a[i] % mod;
}
build();
return t[1].val;
}
int binpow (int a, int b) {
if (b == 0)
return 1;
if (b & 1)
return binpow(a, b - 1) * 1ll * a % mod;
int res = binpow(a, b >> 1);
return res * 1ll * res % mod;
}
void push (int v, int tl, int tr) {
t[v].mx += t[v].add;
t[v].val = t[v].val * 1ll * t[v].must % mod;
if (tl != tr) {
t[v + v].add += t[v].add;
t[v + v + 1].add += t[v].add;
t[v + v].must = t[v + v].must * 1ll * t[v].must % mod;
t[v + v + 1].must = t[v + v + 1].must * 1ll * t[v].must % mod;
}
t[v].must = 1;
t[v].add = 0;
}
void update (int l, int r, long double val, int mult, int v = 1, int tl = 0, int tr = n - 1) {
push(v, tl, tr);
if (l > tr || tl > r)
return;
if (l <= tl && tr <= r) {
t[v].add += val;
t[v].must = t[v].must * 1ll * mult % mod;
push(v, tl, tr);
return;
}
int tm = (tl + tr) >> 1;
update(l, r, val, mult, v + v, tl, tm);
update(l, r, val, mult, v + v + 1, tm + 1, tr);
if (t[v + v].mx - t[v + v + 1].mx > eps) {
t[v].val = t[v + v].val;
t[v].mx = t[v + v].mx;
} else {
t[v].val = t[v + v + 1].val;
t[v].mx = t[v + v + 1].mx;
}
}
int updateX(int pos, int val) {
update(pos, n - 1, -log10(a[pos] + eps), binpow(a[pos], mod - 2) );
a[pos] = val;
update(pos, n - 1, log10(a[pos] + eps), a[pos]);
return t[1].val;
}
int updateY(int pos, int val) {
update(pos, pos, -log10(b[pos] + eps), binpow(b[pos], mod - 2));
b[pos] = val;
update(pos, pos, log10(b[pos] + eps), b[pos]);
return t[1].val;
}
