#include "horses.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<ll,ll>
#define X first
#define Y second
const int N = 500000 + 5;
const int mod = 1000000007;
const int limit = 1000000000;
int n, request, type, x, y, u, v, k;
int a[N], b[N], Xarr[N], Yarr[N], t[4 * N], lazy[4 * N], tTwo[4 * N];
set<int> se;
set<int>::iterator it;
int mul(int x, int y) {
return int((1LL * x * y) % mod);
}
int luythua(int x, int nexp) {
int c = 1;
while (nexp) {
if (nexp & 1) c = mul(c, x);
x = mul(x, x);
nexp >>= 1;
}
return c;
}
void down(int id) {
if (lazy[id] != 1) {
lazy[id << 1] = mul(lazy[id << 1], lazy[id]);
lazy[id << 1 | 1] = mul(lazy[id << 1 | 1], lazy[id]);
tTwo[id << 1] = mul(tTwo[id << 1], lazy[id]);
tTwo[id << 1 | 1] = mul(tTwo[id << 1 | 1], lazy[id]);
lazy[id] = 1;
}
}
// update_range uses globals u,v,k like original
void update_range(int id, int l, int r) {
if (u > r || v < l) return;
if (u <= l && r <= v) {
tTwo[id] = mul(tTwo[id], k);
lazy[id] = mul(lazy[id], k);
return;
}
down(id);
int m = (l + r) >> 1;
update_range(id << 1, l, m);
update_range(id << 1 | 1, m + 1, r);
}
// update_point uses globals u,k: set t at leaf u to k
void update_point(int id, int l, int r) {
if (l == r) {
t[id] = k;
return;
}
int m = (l + r) >> 1;
if (u <= m) update_point(id << 1, l, m);
else update_point(id << 1 | 1, m + 1, r);
t[id] = max(t[id << 1], t[id << 1 | 1]);
}
// get_range uses globals u,v
int get_range(int id, int l, int r) {
if (u > r || v < l) return 0;
if (u <= l && r <= v) return t[id];
down(id);
int m = (l + r) >> 1;
return max(get_range(id << 1, l, m), get_range(id << 1 | 1, m + 1, r));
}
// get_point uses global u
int get_point(int id, int l, int r) {
if (l == r) return tTwo[id];
down(id);
int m = (l + r) >> 1;
if (u <= m) return get_point(id << 1, l, m);
else return get_point(id << 1 | 1, m + 1, r);
}
// build using pref_mod to avoid side effects of modifying cur inside recursion
function<void(int,int,int, const vector<int>&)> build; // forward
int init(int nn, int aarr[], int barr[]) {
::n = nn;
for (int i = 0; i < n; ++i) {
Xarr[i] = aarr[i];
Yarr[i] = barr[i];
}
// prepare prefix modulo array (prefix_mod[i] = X[0]*...*X[i-1] mod)
vector<int> prefix_mod(n + 1);
prefix_mod[0] = 1;
for (int i = 1; i <= n; ++i) prefix_mod[i] = mul(prefix_mod[i - 1], Xarr[i - 1]);
// init segment tree arrays (clean)
int SZ = 4 * (n + 5);
for (int i = 0; i < SZ; ++i) {
t[i] = 0;
lazy[i] = 1;
tTwo[i] = 1;
}
// build function (uses prefix_mod)
build = [&](int id, int l, int r, const vector<int> &pref_mod) {
lazy[id] = 1;
tTwo[id] = 1;
if (l == r) {
if (l == 0) t[id] = 1;
else t[id] = Yarr[l - 1];
tTwo[id] = pref_mod[l]; // prefix mod for leaf l
return;
}
int m = (l + r) >> 1;
build(id << 1, l, m, pref_mod);
build(id << 1 | 1, m + 1, r, pref_mod);
t[id] = max(t[id << 1], t[id << 1 | 1]);
};
// build tree
build(1, 0, n, prefix_mod);
// fill set se
se.clear();
se.insert(0);
for (int i = 0; i < n; ++i) if (Xarr[i] != 1) se.insert(i + 1);
// find best: iterate as you requested: multiply cur by X[old-1] then --it then check pos=*it
it = prev(se.end());
int best = *it;
// ma: pair(maxY, den) where den is cur-ref per your semantics; init with last element
u = *it; v = n;
pii ma = make_pair(get_range(1, 0, n), 1);
long long cur = 1;
while (it != se.begin()) {
int old = *it;
if (old) {
cur = cur * 1LL * Xarr[old - 1];
if (cur >= limit) cur = limit; // cap to avoid overflow
}
--it;
int pos = *it;
u = pos; v = n;
int temp = get_range(1, 0, n);
// compare ratios: ma.first/ma.second < temp/cur
if ((long long)ma.first * cur < (long long)temp * ma.second) {
best = pos;
ma.first = temp;
ma.second = 1; // follow your desired reset behavior
cur = 1;
}
}
u = best;
int prefMod = get_point(1, 0, n);
u = best; v = n;
int ans = mul(prefMod, get_range(1, 0, n));
return ans;
}
int updateX(int pos0, int val) {
int pos = pos0 + 1;
if (Xarr[pos - 1] != val) {
if (Xarr[pos - 1] == 1) se.insert(pos);
k = mul(luythua(Xarr[pos - 1], mod - 2), val); // multiplier modulo
u = pos; v = n;
update_range(1, 0, n);
Xarr[pos - 1] = val;
if (val == 1) se.erase(pos);
}
// find best again with same iteration logic
it = prev(se.end());
int best = *it;
u = *it; v = n;
pii ma = make_pair(get_range(1, 0, n), 1);
long long cur = 1;
while (it != se.begin()) {
int old = *it;
if (old) {
cur = cur * 1LL * Xarr[old - 1];
if (cur >= limit) cur = limit;
}
--it;
int pos2 = *it;
u = pos2; v = n;
int temp = get_range(1, 0, n);
if ((long long)ma.first * cur < (long long)temp * ma.second) {
best = pos2;
ma.first = temp;
ma.second = 1;
cur = 1;
}
}
u = best;
int prefMod = get_point(1, 0, n);
u = best; v = n;
return mul(prefMod, get_range(1, 0, n));
}
int updateY(int pos0, int val) {
int pos = pos0 + 1;
if (Yarr[pos - 1] != val) {
u = pos; k = val;
update_point(1, 0, n); // set t at leaf pos to val
Yarr[pos - 1] = val;
}
// find best again
it = prev(se.end());
int best = *it;
u = *it; v = n;
pii ma = make_pair(get_range(1, 0, n), 1);
long long cur = 1;
while (it != se.begin()) {
int old = *it;
if (old) {
cur = cur * 1LL * Xarr[old - 1];
if (cur >= limit) cur = limit;
}
--it;
int pos2 = *it;
u = pos2; v = n;
int temp = get_range(1, 0, n);
if ((long long)ma.first * cur < (long long)temp * ma.second) {
best = pos2;
ma.first = temp;
ma.second = 1;
cur = 1;
}
}
u = best;
int prefMod = get_point(1, 0, n);
u = best; v = n;
return mul(prefMod, get_range(1, 0, n));
}
