#include <bits/stdc++.h>
#include "horses.h"
using namespace std;
typedef long long ll;
typedef vector<int> vi;
#define x first
#define y second
const int MOD = 1000000007;
const int base = 1000000000;
const int base_digits = 9;
struct Int {
vector<int> a;
int sign;
Int() :
sign(1) {
}
Int(long long v) {
*this = v;
}
void operator=(const Int &v) {
sign = v.sign;
a = v.a;
}
void operator=(long long v) {
sign = 1;
a.clear();
if (v < 0)
sign = -1, v = -v;
for (; v > 0; v = v / base)
a.push_back(v % base);
}
Int operator+(const Int &v) const {
if (sign == v.sign) {
Int res = v;
for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
if (i == (int) res.a.size())
res.a.push_back(0);
res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
carry = res.a[i] >= base;
if (carry)
res.a[i] -= base;
}
return res;
}
return *this - (-v);
}
Int operator-(const Int &v) const {
if (sign == v.sign) {
if (abs() >= v.abs()) {
Int res = *this;
for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
carry = res.a[i] < 0;
if (carry)
res.a[i] += base;
}
res.trim();
return res;
}
return -(v - *this);
}
return *this + (-v);
}
void operator*=(int v) {
if (v < 0) {
sign = -sign, v = -v;
}
for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
if (i == (int) a.size())
a.push_back(0);
long long cur = a[i] * (long long) v + carry;
carry = (int) (cur / base);
a[i] = (int) (cur % base);
}
trim();
}
Int operator*(int v) const {
Int res = *this;
res *= v;
return res;
}
void operator*=(long long v) {
if (v < 0) {
sign = -sign, v = -v;
}
for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
if (i == (int) a.size())
a.push_back(0);
long long cur = a[i] * (long long) v + carry;
carry = (int) (cur / base);
a[i] = (int) (cur % base);
}
trim();
}
Int operator*(long long v) const {
Int res = *this;
res *= v;
return res;
}
friend pair<Int, Int> divmod(const Int &a1, const Int &b1) {
int norm = base / (b1.a.back() + 1);
Int a = a1.abs() * norm;
Int b = b1.abs() * norm;
Int q, r;
q.a.resize(a.a.size());
for (int i = a.a.size() - 1; i >= 0; i--) {
r *= base;
r += a.a[i];
int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
int d = ((long long) base * s1 + s2) / b.a.back();
r -= b * d;
while (r < 0) {
r += b, --d;
}
q.a[i] = d;
}
q.sign = a1.sign * b1.sign;
r.sign = a1.sign;
q.trim();
r.trim();
return make_pair(q, r / norm);
}
Int operator/(const Int &v) const {
return divmod(*this, v).first;
}
Int operator%(const Int &v) const {
return divmod(*this, v).second;
}
void operator/=(int v) {
if (v < 0) {
sign = -sign, v = -v;
}
for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
long long cur = a[i] + rem * (long long) base;
a[i] = (int) (cur / v);
rem = (int) (cur % v);
}
trim();
}
Int operator/(int v) const {
Int res = *this;
res /= v;
return res;
}
int operator%(int v) const {
if (v < 0)
v = -v;
int m = 0;
for (int i = a.size() - 1; i >= 0; --i) {
m = (a[i] + m * (long long) base) % v;
}
return m * sign;
}
void operator+=(const Int &v) {
*this = *this + v;
}
void operator-=(const Int &v) {
*this = *this - v;
}
void operator*=(const Int &v) {
*this = *this * v;
}
void operator/=(const Int &v) {
*this = *this / v;
}
bool operator<(const Int &v) const {
if (sign != v.sign)
return sign < v.sign;
if (a.size() != v.a.size())
return a.size() * sign < v.a.size() * v.sign;
for (int i = a.size() - 1; i >= 0; i--)
if (a[i] != v.a[i])
return a[i] * sign < v.a[i] * sign;
return false;
}
bool operator>(const Int &v) const {
return v < *this;
}
bool operator<=(const Int &v) const {
return !(v < *this);
}
bool operator>=(const Int &v) const {
return !(*this < v);
}
bool operator==(const Int &v) const {
return !(*this < v) && !(v < *this);
}
bool operator!=(const Int &v) const {
return *this < v || v < *this;
}
void trim() {
while (!a.empty() && !a.back())
a.pop_back();
if (a.empty())
sign = 1;
}
bool isZero() const {
return a.empty() || (a.size() == 1 && !a[0]);
}
Int operator-() const {
Int res = *this;
res.sign = -sign;
return res;
}
Int abs() const {
Int res = *this;
res.sign *= res.sign;
return res;
}
long long longValue() const {
long long res = 0;
for (int i = a.size() - 1; i >= 0; i--)
res = res * base + a[i];
return res * sign;
}
static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
vector<long long> p(max(old_digits, new_digits) + 1);
p[0] = 1;
for (int i = 1; i < (int) p.size(); i++) {
p[i] = p[i - 1] * 10;
}
vector<int> res;
long long cur = 0;
int cur_digits = 0;
for (int i = 0; i < (int) a.size(); i++) {
cur += a[i] * p[cur_digits];
cur_digits += old_digits;
while (cur_digits >= new_digits) {
res.push_back(int(cur % p[new_digits]));
cur /= p[new_digits];
cur_digits -= new_digits;
}
}
res.push_back((int) cur);
while (!res.empty() && !res.back()) {
res.pop_back();
}
return res;
}
typedef vector<long long> vll;
static vll karatsubaMultiply(const vll &a, const vll &b) {
int n = a.size();
vll res(n + n);
if (n <= 32) {
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
res[i + j] += a[i] * b[j];
}
return res;
}
int k = n >> 1;
vll a1(a.begin(), a.begin() + k);
vll a2(a.begin() + k, a.end());
vll b1(b.begin(), b.begin() + k);
vll b2(b.begin() + k, b.end());
vll a1b1 = karatsubaMultiply(a1, b1);
vll a2b2 = karatsubaMultiply(a2, b2);
for (int i = 0; i < k; i++)
a2[i] += a1[i];
for (int i = 0; i < k; i++)
b2[i] += b1[i];
vll r = karatsubaMultiply(a2, b2);
for (int i = 0; i < (int) a1b1.size(); i++)
r[i] -= a1b1[i];
for (int i = 0; i < (int) a2b2.size(); i++)
r[i] -= a2b2[i];
for (int i = 0; i < (int) r.size(); i++)
res[i + k] += r[i];
for (int i = 0; i < (int) a1b1.size(); i++)
res[i] += a1b1[i];
for (int i = 0; i < (int) a2b2.size(); i++)
res[i + n] += a2b2[i];
return res;
}
Int operator*(const Int &v) const {
vector<int> a6 = convert_base(this->a, base_digits, 6);
vector<int> b6 = convert_base(v.a, base_digits, 6);
vll a(a6.begin(), a6.end());
vll b(b6.begin(), b6.end());
while (a.size() < b.size())
a.push_back(0);
while (b.size() < a.size())
b.push_back(0);
while (a.size() & (a.size() - 1))
a.push_back(0), b.push_back(0);
vll c = karatsubaMultiply(a, b);
Int res;
res.sign = sign * v.sign;
for (int i = 0, carry = 0; i < (int) c.size(); i++) {
long long cur = c[i] + carry;
res.a.push_back((int) (cur % 1000000));
carry = (int) (cur / 1000000);
}
res.a = convert_base(res.a, 6, base_digits);
res.trim();
return res;
}
};
struct node {
int l, r;
Int did;
Int kart;
Int dalint;
node *left = nullptr;
node *right = nullptr;
node(int a, int b): l(a), r(b) {
did = 1;
kart = 1;
dalint = 1;
if (l != r) {
left = new node(l, (l + r) / 2);
right = new node((l + r) / 2 + 1, r);
}
}
inline void push() {
if (kart == 1 and dalint == 1) return;
if (dalint != 1) did /= dalint;
did *= kart;
if (l != r) {
left->kart *= kart;
left->dalint *= dalint;
right->kart *= kart;
right->dalint *= dalint;
}
kart = 1;
dalint = 1;
}
inline void upd() {
if (l == r) return;
did = max(left->did, right->did);
}
void daug(int a, int b, Int val) {
push();
if (b < l or r < a) return;
if (a <= l and r <= b) {
kart *= val;
push();
} else {
left->daug(a, b, val);
right->daug(a, b, val);
did = (left->did > right->did ? left->did : right->did);
}
}
void dal(int a, int b, Int val) {
push();
if (b < l or r < a) return;
if (a <= l and r <= b) {
dalint *= val;
push();
} else {
left->dal(a, b, val);
right->dal(a, b, val);
did = (left->did > right->did ? left->did : right->did);
}
}
};
node *medis = nullptr;
vi x, y;
int n;
int init(int N, int X[], int Y[]) {
medis = new node(0, N - 1);
n = N;
for (int i = 0; i < N; ++i)
{
medis->daug(i, N - 1, (Int)X[i]);
medis->daug(i, i, (Int)Y[i]);
x.emplace_back(X[i]);
y.emplace_back(Y[i]);
}
ll ats = divmod(medis->did, MOD).y.longValue();
return (int)ats;
}
int updateX(int pos, int val) {
medis->dal(pos, n - 1, x[pos]);
x[pos] = val;
medis->daug(pos, n - 1, x[pos]);
ll ats = divmod(medis->did, MOD).y.longValue();
return (int)ats;
}
int updateY(int pos, int val) {
medis->dal(pos, pos, y[pos]);
y[pos] = val;
medis->daug(pos, pos, y[pos]);
ll ats = divmod(medis->did, MOD).y.longValue();
return (int)ats;
}
