#include <bits/stdc++.h>
//#include "horses.h"
#pragma GCC optimize("O2")
#pragma GCC target("avx2")
using namespace std;
const long long mod = 1e9 + 7;
struct medis{
struct node{
int l, r;
int sand = 1;
int vntCnt = 0;
int maxY = 0;
};
int n;
int dbInd = 0;
vector<node> tree;
void build(int v){
if(v >= n){
tree[v].l = tree[v].r = dbInd++;
}else{
build(v*2); build(v*2+1);
tree[v].l = tree[v*2].l;
tree[v].r = tree[v*2+1].r;
}
}
medis(int dd){
n = dd;
tree.resize(2*n+1);
build(1);
}
void changeX(int v, int l, int r, int x){
if(l <= tree[v].l && tree[v].r <= r){
tree[v].sand = x;
tree[v].vntCnt = (x != 1);
}else if(r < tree[v].l || tree[v].r < l){
return;
}else{
changeX(v*2, l, r, x);
changeX(v*2+1, l, r, x);
tree[v].sand = 1ll * tree[v*2].sand * tree[v*2+1].sand % mod;
tree[v].vntCnt = tree[v*2].vntCnt + tree[v*2+1].vntCnt;
}
}
void changeY(int v, int l, int r, int x){
if(l <= tree[v].l && tree[v].r <= r){
tree[v].maxY = x;
}else if(r < tree[v].l || tree[v].r < l){
return;
}else{
changeY(v*2, l, r, x);
changeY(v*2+1, l, r, x);
tree[v].maxY = max(tree[v*2].maxY, tree[v*2+1].maxY);
}
}
int getSand(int v, int l, int r){
if(l <= tree[v].l && tree[v].r <= r){
return tree[v].sand;
}else if(r < tree[v].l || tree[v].r < l){
return 1;
}else{
return 1ll * getSand(v*2, l, r) * getSand(v*2+1, l, r) % mod;
}
}
long long getMax(int v, int l, int r){
if(l <= tree[v].l && tree[v].r <= r){
return tree[v].maxY;
}else if(r < tree[v].l || tree[v].r < l){
return 1;
}else{
return max(getMax(v*2, l, r), getMax(v*2+1, l, r));
}
}
int get1(int v, int l, int r){
if(l <= tree[v].l && tree[v].r <= r){
return tree[v].vntCnt;
}else if(r < tree[v].l || tree[v].r < l){
return 0;
}else{
return get1(v*2, l, r) + get1(v*2+1, l, r);
}
}
int fd(int v, int sm){ // rasti kairiausia x, kad suf[x; n] <= sm
if(tree[v].l == tree[v].r){
if(tree[v].vntCnt == 1 && sm == 0) return tree[v].l + 1;
return tree[v].l;
}
if(tree[v*2+1].vntCnt < sm){
return fd(v*2, sm-tree[v*2+1].vntCnt);
}else if(tree[v*2+1].vntCnt == sm){
return fd(v*2, sm-tree[v*2+1].vntCnt);
}else{
return fd(v*2+1, sm);
}
}
};
const int dydis = 5e5 + 1;
medis tree(dydis);
int n;
int rt, tr;
pair<int, vector<pair<int, int> > > last30(int n){
int lastNotIn = n-1;
vector<pair<int, int> > ret;
int kk = 0;
for(int i = 0; i < 62; i++){
if(lastNotIn == -1) break;
if(tree.getSand(1, lastNotIn, lastNotIn) == 1){
rt = lastNotIn;
tr = tree.get1(1, lastNotIn, dydis-1);
rt = tree.fd(1, tr);
ret.push_back({1, tree.getMax(1, rt, lastNotIn)});
lastNotIn = rt-1;
}else{
ret.push_back({tree.getSand(1, lastNotIn, lastNotIn), tree.getMax(1, lastNotIn, lastNotIn)});
lastNotIn--;
kk++;
}
if(kk > 30) break;
}
reverse(ret.begin(), ret.end());
long long bv = 1;
if(lastNotIn != -1) bv = tree.getSand(1, 0, lastNotIn);
return {bv, ret};
}
long long h;
int curMax;
long long B;
bool did;
long long turiButi, ret;
long long get(){
auto rk = last30(n);
h = rk.first;
auto mas = rk.second;
curMax = 0;
for(int i = 0; i < (int)mas.size(); i++){
B = 1;
did = 0;
for(int j = i+1; j < (int) mas.size(); j++){
B *= mas[j].first;
if(mas[j].second >= mas[i].second){
curMax = j;
did = 1;
i = j-1; break;
}
turiButi = mas[i].second / mas[j].second + 1;
if(B >= turiButi){
i = j-1;
did = 1;
curMax = j;
break;
}
}
if(!did) break;
}
ret = h;
for(int i = 0; i <= curMax; i++){
ret = ret * mas[i].first % mod;
}
ret = ret * mas[curMax].second % mod;
return ret;
}
int init(int N, int X[], int Y[]) {
n = N;
for(int i = 0; i < n; i++){
tree.changeX(1, i, i, X[i]);
tree.changeY(1, i, i, Y[i]);
}
return get();
}
int updateX(int pos, int val) {
tree.changeX(1, pos, pos, val);
return get();
}
int updateY(int pos, int val) {
tree.changeY(1, pos, pos, val);
return get();
}
