#include "horses.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod = 1e9 + 7;
const int lim = 5e5 + 5;
int power(int a, int b){
int ans = 1;
for(; b > 0; b >>= 1, a = 1LL * a * a % mod){
if(b & 1){
ans = 1LL * ans * a % mod;
}
}
return ans;
}
int n, pl[lim << 2], pr[lim << 2], temp[lim << 2], st[lim << 2], x[lim], x_st[lim << 2], y[lim], bit[lim];
int get_bit(int p){
int ans = 1;
for(; p > 0; p -= p & -p){
ans = 1LL * ans * bit[p] % mod;
}
return ans;
}
void update_bit(int p, int x){
for(; p <= n; p += p & -p){
bit[p] = 1LL * bit[p] * x % mod;
}
}
int get_x_prod(int id, int l, int r, int u, int v){
if(l > v || r < u){
return 1;
}
if(u <= l && v >= r){
return x_st[id];
}
int m = (l + r) >> 1, left = get_x_prod(id << 1, l, m, u, v);
if(left == mod){
return mod;
}
return min(ll(mod), 1LL * left * get_x_prod(id << 1 | 1, m + 1, r, u, v));
}
int merge(int id){
int l = st[id << 1], r = st[id << 1 | 1];
if(l == 0){
return r;
}
if(r == 0){
return l;
}
if(pl[id] != l || pr[id] != r){
temp[id] = get_x_prod(1, 1, n, l + 1, r);
}
return 1LL * temp[id] * y[r] < ll(y[l]) ? l : r;
}
void update_X(int id, int l, int r, int p, int X){
if(l == r){
update_bit(l, 1LL * power(x[l], mod - 2) * X % mod);
x[st[id] = l] = X;
x_st[id] = X;
return;
}
int m = (l + r) >> 1;
if(m < p){
update_X(id << 1 | 1, m + 1, r, p, X);
}
else{
update_X(id << 1, l, m, p, X);
}
st[id] = merge(id);
x_st[id] = min(ll(mod), 1LL * x_st[id << 1] * x_st[id << 1 | 1]);
}
void update_Y(int p, int Y){
y[p] = Y;
int id = 1, l = 1, r = n;
while(l < r){
int m = (l + r) >> 1;
id <<= 1;
if(m < p){
l = m + 1;
id |= 1;
}
else{
r = m;
}
}
while((id >>= 1) > 0){
st[id] = merge(id);
}
}
int init(int N, int X[], int Y[]){
n = N;
fill(bit, bit + lim, 1);
for(int i = 1; i <= n; i++){
y[i] = Y[i - 1];
update_bit(i, x[i] = X[i - 1]);
}
memset(pl, -1, sizeof(pl));
memset(pr, -1, sizeof(pr));
fill(x_st, x_st + (lim << 2), 1);
for(int i = 1; i <= n; i++){
update_X(1, 1, n, i, X[i - 1]);
}
return 1LL * get_bit(st[1]) * y[st[1]] % mod;
}
int updateX(int pos, int val){
update_X(1, 1, n, pos + 1, val);
return 1LL * get_bit(st[1]) * y[st[1]] % mod;
}
int updateY(int pos, int val){
update_Y(pos + 1, val);
return 1LL * get_bit(st[1]) * y[st[1]] % mod;
}
