#include "horses.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 5e5+10;
const int MOD = 1e9+7;
int n; ll mulz[N];
double X[N], Y[N];
double tmp[N];
struct SGT1{
struct nude{
int idx;
double mx, lazy;
}t[N<<2];
void build(int node, int L, int R) {
t[node].lazy = 0;
if(L == R) {
t[node].mx = tmp[L];
t[node].idx = L;
return;
} int mid = (L+R)>>1, lc = node<<1, rc = lc|1;
build(lc, L, mid); build(rc, mid+1, R);
if(t[lc].mx > t[rc].mx) {
t[node].mx = t[lc].mx;
t[node].idx = t[lc].idx;
} else {
t[node].mx = t[rc].mx;
t[node].idx = t[rc].idx;
}
}
void shift(int node) {
int lc = node<<1, rc = lc|1;
t[lc].mx += t[node].lazy;
t[rc].mx += t[node].lazy;
t[lc].lazy += t[node].lazy;
t[rc].lazy += t[node].lazy;
t[node].lazy = 0;
if(t[lc].mx > t[rc].mx) {
t[node].mx = t[lc].mx;
t[node].idx = t[lc].idx;
} else {
t[node].mx = t[rc].mx;
t[node].idx = t[rc].idx;
}
}
void upd(int node, int L, int R, int l, int r, double v) {
if(r < L || R < l) return;
if(l <= L && R <= r) {
t[node].lazy += v;
t[node].mx += v;
return;
} if(t[node].lazy != 0) shift(node);
int mid = (L+R)>>1, lc = node<<1, rc = lc|1;
upd(lc, L, mid, l, r, v);
upd(rc, mid+1, R, l, r, v);
if(t[lc].mx > t[rc].mx) {
t[node].mx = t[lc].mx;
t[node].idx = t[lc].idx;
} else {
t[node].mx = t[rc].mx;
t[node].idx = t[rc].idx;
}
}
int get() { return t[1].idx; }
}opt;
struct SGT2{
ll t[N<<2], lazy[N<<2];
void build(int node, int L, int R) {
lazy[node] = 1;
if(L == R) return void(t[node] = mulz[L]);
int mid = (L+R)>>1, lc = node<<1, rc = lc|1;
build(lc, L, mid); build(rc, mid+1, R);
t[node] = t[lc] * t[rc] % MOD;
}
void shift(int node) {
int lc = node<<1, rc = lc|1;
t[lc] = t[lc] * lazy[node] % MOD;
t[rc] = t[rc] * lazy[node] % MOD;
lazy[lc] = lazy[lc] * lazy[node] % MOD;
lazy[rc] = lazy[rc] * lazy[node] % MOD;
lazy[node] = 1;
}
void upd(int node, int L, int R, int l, int r, ll v) {
if(r < L || R < l) return;
if(l <= L && R <= r) {
t[node] = t[node] * v % MOD;
lazy[node] = lazy[node] * v % MOD;
return;
} if(lazy[node] != 1) shift(node);
int mid = (L+R)>>1, lc = node<<1, rc = lc|1;
upd(lc, L, mid, l, r, v); upd(rc, mid+1, R, l, r, v);
t[node] = t[lc] * t[rc] % MOD;
}
ll get(int node, int L, int R, int pos) {
if(L == R) return t[node];
if(lazy[node] != 1) shift(node);
int mid = (L+R)>>1, lc = node<<1, rc = lc|1;
if(pos <= mid) return get(lc, L, mid, pos);
return get(rc, mid+1, R, pos);
}
}mul;
int init(int _N, int _X[], int _Y[]) {
n = _N;
for(int i = 1; i <= n; i++) X[i] = _X[i-1], Y[i] = _Y[i-1];
for(int i = 1; i <= n; i++)
tmp[i] = tmp[i-1] + log(X[i]);
for(int i = 1; i <= n; i++)
tmp[i] += log(Y[i]);
mulz[0] = 1;
for(int i = 1; i <= n; i++)
mulz[i] = mulz[i-1] * (ll)X[i] % MOD;
for(int i = 1; i <= n; i++)
mulz[i] = mulz[i] * (ll)Y[i] % MOD;
opt.build(1,1,n);
mul.build(1,1,n);
int idx = opt.get();
return mul.get(1,1,n,idx);
}
ll powmod(ll a, ll b) {
ll r = 1;
while(b) {
if(b & 1) r = r * a % MOD;
a = a * a % MOD;
b>>=1;
} return r;
}
ll modinv(ll x) { return powmod(x,MOD-2); }
int updateX(int pos, int val) {
pos++;
double del = log((double)val) - log((double)X[pos]);
opt.upd(1,1,n,pos,n,del);
ll det = (ll)val * modinv((ll)X[pos]) % MOD;
mul.upd(1,1,n,pos,n,det);
X[pos] = val;
int idx = opt.get();
return mul.get(1,1,n,idx);
}
int updateY(int pos, int val) {
pos++;
double del = log((double)val) - log((double)Y[pos]);
opt.upd(1,1,n,pos,pos,del);
ll det = (ll)val * modinv((ll)Y[pos]) % MOD;
mul.upd(1,1,n,pos,pos,det);
Y[pos] = val;
int idx = opt.get();
return mul.get(1,1,n,idx);
}
