#include "horses.h"
#include<bits/stdc++.h>
using namespace std;
#define mp make_pair
#define INF 10000000
#define MOD 1000000007ll
#define MID ((l+r)/2)
#define HASHMOD 2305843009213693951
#define ll long long
#define ull unsigned long long
#define F first
#define S second
typedef pair<ll, ll> ii;
typedef pair<ii, int> iii;
typedef vector<ll> vi;
typedef vector<ii> vii;
typedef map<int, int> mii;
#define EPS 1e-6
#define FOR(i,n) for(int i=0;i<((int)(n));i++)
#define FORi(i,a,b) for(int i=((int)(a));i<((int)(b));i++)
#define FOA(v, a) for(auto v : a)
ll mpow(ll a, ll b){
if(b==0) return 1;
if(b==1) return a;
ll z = mpow(a, b/2);
z*=z;
z%=MOD;
if(b%2) z*=a;
return z%MOD;
}
ll modinv(ll x){
return mpow(x, MOD-2);
}
struct seg_tree{
typedef long double T;
struct node{
T val;
T laz;
ll val_mod;
ll laz_mod=1;
int left=-1;
int right=-1;
node() {val=0, laz=0, left=-1, right=-1;}
node(T v, ll q) {val=v, val_mod=q, laz=0, laz_mod=1, right=-1, left=-1;}
node(T v) {val=v, val_mod=0, laz=0, laz_mod=1, right=-1, left=-1;}
};
vector<node> seg;
static inline int N;
const int RAND_VALUE=0;
seg_tree(int n){N=n, seg.assign(1, node());}
inline node merge(node par, node a, node b){
node ret;
ret.left = par.left, ret.right = par.right;
ret.val = max(a.val, b.val);
if(a.val>b.val) ret.val_mod = a.val_mod;
else ret.val_mod = b.val_mod;
return ret;
}
inline void update_node(ll ind, ll val, ll val_prev, int l, int r){
//cout<<"change "<<l<<" "<<r<<" by "<<log(val)<<" "<<log(val_prev)<<endl;
seg[ind].val += (log(val)-log(val_prev));
seg[ind].val_mod = ((seg[ind].val_mod * modinv(val_prev))%MOD * val)%MOD;
seg[ind].laz += (log(val)-log(val_prev));
seg[ind].laz_mod *= (modinv(val_prev) * val)%MOD;
seg[ind].laz_mod %= MOD;
}
inline void down(node &par, int l, int r){
if(par.laz && par.laz_mod!=1){
seg[par.left].val += par.laz;
seg[par.right].val += par.laz;
seg[par.left].laz += par.laz;
seg[par.right].laz += par.laz;
seg[par.left].val_mod = (seg[par.left].val_mod * par.laz_mod)%MOD;
seg[par.right].val_mod = (seg[par.right].val_mod * par.laz_mod)%MOD;
seg[par.left].laz_mod *= par.laz_mod;
seg[par.left].laz_mod %= MOD;
seg[par.right].laz_mod *= par.laz_mod;
seg[par.right].laz_mod %= MOD;
}
par.laz = 0;
par.laz_mod = 1;
}
inline void create_children(int ind){
node par = seg[ind];
if(par.left==-1) par.left=seg.size(), seg.push_back(node());
if(par.right==-1) par.right=seg.size(), seg.push_back(node());
seg[ind] = par;
}
void build(vector<T>& arr, vector<ll> arr_mod, int l=0, int r=N-1, int ind=0){
if(l==r) seg[ind] = node(arr[l], arr_mod[l]);
else{
create_children(ind);
build(arr,arr_mod, l,MID,seg[ind].left);
build(arr,arr_mod, MID+1,r,seg[ind].right);
seg[ind] = merge(seg[ind], seg[seg[ind].left], seg[seg[ind].right]);
}
}
void update(int rl, int rr, ll val, ll val_prev, int l=0, int r=N-1, int ind=0){
if(rl<=l && r<=rr) update_node(ind, val, val_prev,l,r);
else if(rr<l || r<rl) return;
else{
create_children(ind);
down(seg[ind],l,r);
update(rl,rr,val, val_prev,l,MID,seg[ind].left);
update(rl,rr,val, val_prev, MID+1,r,seg[ind].right);
seg[ind] = merge(seg[ind], seg[seg[ind].left], seg[seg[ind].right]);
}
}
node _query(int rl, int rr, int l=0, int r=N-1, int ind=0){
if(rl<=l && r<=rr) return seg[ind];
else if(rl>r || l>rr) return RAND_VALUE;
else{
create_children(ind);
down(seg[ind],l,r);
return merge(seg[ind], _query(rl, rr, l, MID, seg[ind].left), _query(rl,rr,MID+1,r,seg[ind].right));
}
}
ll query(int l, int r){
return _query(l,r).val_mod;
}
};
int n;
vi x,y;
seg_tree seg(n);
int init(int N, int X[], int Y[]) {
n = N;
seg.N = n;
x.resize(n);
y.resize(n);
FOR(i,n) x[i] = X[i], y[i] = Y[i];
vector<long double> ly(n);
vi my(n);
ly[0] = log(x[0]);
my[0] = x[0];
FORi(i,1,n) ly[i] = ly[i-1] + log(x[i]);
FORi(i,1,n) my[i] = (my[i-1] * x[i])%MOD;
FOR(i,n) my[i] = (my[i]*y[i])%MOD;
FOR(i,n) ly[i] += log(y[i]);
seg.build(ly, my);
//FOR(i,n) cout<<seg.query(i,i)<<" "; cout<<endl;
return seg.query(0, n-1);
}
int updateX(int pos, int val) {
//FOR(i,n) cout<<seg._query(i,i).val_mod<<" "; cout<<endl;
//FOR(i,n) seg.query(i,i);
ll pval = x[pos];
x[pos] = val;
seg.update(pos, n-1, val, pval);
//FOR(i,n) cout<<seg._query(i,i).val_mod<<" "; cout<<endl;
//cout<<endl;
return seg.query(0, n-1);
}
int updateY(int pos, int val) {
ll pval = y[pos];
y[pos] = val;
seg.update(pos, pos, val, pval);
return seg.query(0, n-1);
}
