#define PROBLEM "https://yukicoder.me/problems/no/510"
#include <iostream>
#include <vector>
#include "Mylib/AlgebraicStructure/Monoid/dual.cpp"
#include "Mylib/AlgebraicStructure/Monoid/product_matrix.cpp"
#include "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
#include "Mylib/IO/input_tuples.cpp"
#include "Mylib/LinearAlgebra/square_matrix_const_size.cpp"
#include "Mylib/Number/Mint/mint.cpp"
namespace hl = haar_lib;
using mint = hl::modint<1000000007>;
using Mat = hl::square_matrix_const<mint, 4>;
using Monoid = hl::dual_monoid<hl::product_matrix_monoid<Mat>>;
auto f(mint x, mint y) {
Mat ret = {
{1, 0, x, 0},
{0, y, 0, 1},
{0, 2 * y, y * y, 1},
{0, 0, 0, 1}};
return ret;
}
int main() {
int n, q;
std::cin >> n >> q;
hl::segment_tree<Monoid> seg(n);
std::vector<mint> x(n), y(n);
for (int i = 0; i < n; ++i) {
seg.set(i, f(x[i], y[i]));
}
for (auto [c, i] : hl::input_tuples<char, int>(q)) {
if (c == 'x') {
int v;
std::cin >> v;
x[i] = v;
seg.set(i, f(x[i], y[i]));
} else if (c == 'y') {
int v;
std::cin >> v;
y[i] = v;
seg.set(i, f(x[i], y[i]));
} else {
auto m = seg.fold(0, i);
auto ans = dot(m[0], Mat::vector_type({1, 1, 1, 1}));
std::cout << ans << "\n";
}
}
return 0;
}
#line 1 "test/yukicoder/510/main.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/510"
#include <iostream>
#include <vector>
#line 2 "Mylib/AlgebraicStructure/Monoid/dual.cpp"
namespace haar_lib {
template <typename Monoid>
struct dual_monoid {
using value_type = typename Monoid::value_type;
const static Monoid M;
value_type operator()() const { return M(); }
value_type operator()(const value_type &a, const value_type &b) const { return M(b, a); }
};
} // namespace haar_lib
#line 2 "Mylib/AlgebraicStructure/Monoid/product_matrix.cpp"
namespace haar_lib {
template <typename T>
struct product_matrix_monoid {
using value_type = T;
value_type operator()() const { return T::unit(); }
value_type operator()(const value_type &a, const value_type &b) const { return a * b; }
};
} // namespace haar_lib
#line 2 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
#include <algorithm>
#include <cassert>
#include <functional>
#line 6 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
namespace haar_lib {
template <typename Monoid>
class segment_tree {
public:
using value_type = typename Monoid::value_type;
private:
Monoid M_;
int depth_, size_, hsize_;
std::vector<value_type> data_;
public:
segment_tree() {}
segment_tree(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
size_(1 << depth_),
hsize_(size_ / 2),
data_(size_, M_()) {}
auto operator[](int i) const {
assert(0 <= i and i < hsize_);
return data_[hsize_ + i];
}
auto fold(int l, int r) const {
assert(0 <= l and l <= r and r <= hsize_);
value_type ret_left = M_();
value_type ret_right = M_();
int L = l + hsize_, R = r + hsize_;
while (L < R) {
if (R & 1) ret_right = M_(data_[--R], ret_right);
if (L & 1) ret_left = M_(ret_left, data_[L++]);
L >>= 1, R >>= 1;
}
return M_(ret_left, ret_right);
}
auto fold_all() const {
return data_[1];
}
void set(int i, const value_type &x) {
assert(0 <= i and i < hsize_);
i += hsize_;
data_[i] = x;
while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
void update(int i, const value_type &x) {
assert(0 <= i and i < hsize_);
i += hsize_;
data_[i] = M_(data_[i], x);
while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
template <typename T>
void init_with_vector(const std::vector<T> &val) {
data_.assign(size_, M_());
for (int i = 0; i < (int) val.size(); ++i) data_[hsize_ + i] = val[i];
for (int i = hsize_; --i >= 1;) data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
template <typename T>
void init(const T &val) {
init_with_vector(std::vector<value_type>(hsize_, val));
}
private:
template <bool Lower, typename F>
int bound(const int l, const int r, value_type x, F f) const {
std::vector<int> pl, pr;
int L = l + hsize_;
int R = r + hsize_;
while (L < R) {
if (R & 1) pr.push_back(--R);
if (L & 1) pl.push_back(L++);
L >>= 1, R >>= 1;
}
std::reverse(pr.begin(), pr.end());
pl.insert(pl.end(), pr.begin(), pr.end());
value_type a = M_();
for (int i : pl) {
auto b = M_(a, data_[i]);
if ((Lower and not f(b, x)) or (not Lower and f(x, b))) {
while (i < hsize_) {
const auto c = M_(a, data_[i << 1 | 0]);
if ((Lower and not f(c, x)) or (not Lower and f(x, c))) {
i = i << 1 | 0;
} else {
a = c;
i = i << 1 | 1;
}
}
return i - hsize_;
}
a = b;
}
return r;
}
public:
template <typename F = std::less<value_type>>
int lower_bound(int l, int r, value_type x, F f = F()) const {
return bound<true>(l, r, x, f);
}
template <typename F = std::less<value_type>>
int upper_bound(int l, int r, value_type x, F f = F()) const {
return bound<false>(l, r, x, f);
}
};
} // namespace haar_lib
#line 2 "Mylib/IO/input_tuples.cpp"
#include <initializer_list>
#line 4 "Mylib/IO/input_tuples.cpp"
#include <tuple>
#include <utility>
#line 6 "Mylib/IO/input_tuple.cpp"
namespace haar_lib {
template <typename T, size_t... I>
static void input_tuple_helper(std::istream &s, T &val, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(s >> std::get<I>(val)), 0)...};
}
template <typename T, typename U>
std::istream &operator>>(std::istream &s, std::pair<T, U> &value) {
s >> value.first >> value.second;
return s;
}
template <typename... Args>
std::istream &operator>>(std::istream &s, std::tuple<Args...> &value) {
input_tuple_helper(s, value, std::make_index_sequence<sizeof...(Args)>());
return s;
}
} // namespace haar_lib
#line 8 "Mylib/IO/input_tuples.cpp"
namespace haar_lib {
template <typename... Args>
class InputTuples {
struct iter {
using value_type = std::tuple<Args...>;
value_type value;
bool fetched = false;
int N, c = 0;
value_type operator*() {
if (not fetched) {
std::cin >> value;
}
return value;
}
void operator++() {
++c;
fetched = false;
}
bool operator!=(iter &) const {
return c < N;
}
iter(int N) : N(N) {}
};
int N;
public:
InputTuples(int N) : N(N) {}
iter begin() const { return iter(N); }
iter end() const { return iter(N); }
};
template <typename... Args>
auto input_tuples(int N) {
return InputTuples<Args...>(N);
}
} // namespace haar_lib
#line 2 "Mylib/LinearAlgebra/square_matrix_const_size.cpp"
#include <array>
#line 6 "Mylib/LinearAlgebra/square_matrix_const_size.cpp"
namespace haar_lib {
template <typename T, int N>
class vector_const {
public:
using value_type = T;
private:
std::array<T, N> data_;
public:
vector_const() { data_.fill(0); }
vector_const(T value) { data_.fill(value); }
vector_const(std::initializer_list<T> list) {
int i = 0;
for (auto it = list.begin(); it != list.end(); ++it) data_[i++] = *it;
}
vector_const(const vector_const &that) : data_(that.data_) {}
bool operator==(const vector_const &that) { return data_ == that.data_; }
bool operator!=(const vector_const &that) { return !(*this == that); }
auto &operator=(const vector_const &that) {
data_ = that.data_;
return *this;
}
auto &operator+=(const vector_const &that) {
for (int i = 0; i < N; ++i) data_[i] += that.data_[i];
return *this;
}
auto &operator-=(const vector_const &that) {
for (int i = 0; i < N; ++i) data_[i] -= that.data_[i];
return *this;
}
friend auto dot(const vector_const &a, const vector_const &b) {
T ret = 0;
for (int i = 0; i < N; ++i) ret += a.data_[i] * b.data_[i];
return ret;
}
auto operator+(const vector_const &that) const {
return vector_const(*this) += that;
}
auto operator-(const vector_const &that) const {
return vector_const(*this) -= that;
}
auto &operator[](int i) { return data_[i]; }
const auto &operator[](int i) const { return data_[i]; }
auto begin() const { return data_.begin(); }
auto end() const { return data_.end(); }
int size() const { return N; }
friend std::ostream &operator<<(std::ostream &s, const vector_const &a) {
s << "{";
for (auto it = a.data_.begin(); it != a.data_.end(); ++it) {
if (it != a.data_.begin()) s << ",";
s << *it;
}
s << "}";
return s;
}
};
template <typename T, int N>
class square_matrix_const {
public:
using value_type = T;
using vector_type = vector_const<T, N>;
private:
std::array<vector_type, N> data_;
public:
square_matrix_const() {
for (int i = 0; i < N; ++i) data_[i] = vector_type();
}
square_matrix_const(const T &val) {
for (int i = 0; i < N; ++i) data_[i] = vector_type(val);
}
square_matrix_const(std::initializer_list<std::initializer_list<T>> list) {
int i = 0;
for (auto it = list.begin(); it != list.end(); ++it) {
data_[i++] = vector_type(*it);
}
}
square_matrix_const(const square_matrix_const &that) : data_(that.data_) {}
bool operator==(const square_matrix_const &that) const { return data_ == that.data_; }
bool operator!=(const square_matrix_const &that) const { return !(*this == that); }
auto &operator=(const square_matrix_const &that) {
data_ = that.data_;
return *this;
}
auto &operator+=(const square_matrix_const &that) {
for (int i = 0; i < N; ++i) data_[i] += that.data_[i];
return *this;
}
auto &operator-=(const square_matrix_const &that) {
for (int i = 0; i < N; ++i) data_[i] -= that.data_[i];
return *this;
}
auto &operator*=(const square_matrix_const &that) {
square_matrix_const ret;
for (int i = 0; i < N; ++i)
for (int j = 0; j < N; ++j)
for (int k = 0; k < N; ++k)
ret[i][j] += data_[i][k] * that.data_[k][j];
return *this = ret;
}
const auto &operator[](int i) const { return data_[i]; }
auto &operator[](int i) { return data_[i]; }
int size() const { return N; }
static auto unit() {
square_matrix_const ret;
for (int i = 0; i < N; ++i) ret[i][i] = 1;
return ret;
}
auto operator+(const square_matrix_const &that) const {
return square_matrix_const(*this) += that;
}
auto operator-(const square_matrix_const &that) const {
return square_matrix_const(*this) -= that;
}
auto operator*(const square_matrix_const &that) const {
return square_matrix_const(*this) *= that;
}
auto pow(uint64_t p) const {
auto ret = unit();
auto a = *this;
while (p > 0) {
if (p & 1) ret *= a;
a *= a;
p >>= 1;
}
return ret;
}
auto operator*(const vector_type &that) const {
vector_type ret;
for (int i = 0; i < N; ++i) ret[i] = dot(data_[i], that);
return ret;
}
};
} // namespace haar_lib
#line 4 "Mylib/Number/Mint/mint.cpp"
namespace haar_lib {
template <int32_t M>
class modint {
uint32_t val_;
public:
constexpr static auto mod() { return M; }
constexpr modint() : val_(0) {}
constexpr modint(int64_t n) {
if (n >= M)
val_ = n % M;
else if (n < 0)
val_ = n % M + M;
else
val_ = n;
}
constexpr auto &operator=(const modint &a) {
val_ = a.val_;
return *this;
}
constexpr auto &operator+=(const modint &a) {
if (val_ + a.val_ >= M)
val_ = (uint64_t) val_ + a.val_ - M;
else
val_ += a.val_;
return *this;
}
constexpr auto &operator-=(const modint &a) {
if (val_ < a.val_) val_ += M;
val_ -= a.val_;
return *this;
}
constexpr auto &operator*=(const modint &a) {
val_ = (uint64_t) val_ * a.val_ % M;
return *this;
}
constexpr auto &operator/=(const modint &a) {
val_ = (uint64_t) val_ * a.inv().val_ % M;
return *this;
}
constexpr auto operator+(const modint &a) const { return modint(*this) += a; }
constexpr auto operator-(const modint &a) const { return modint(*this) -= a; }
constexpr auto operator*(const modint &a) const { return modint(*this) *= a; }
constexpr auto operator/(const modint &a) const { return modint(*this) /= a; }
constexpr bool operator==(const modint &a) const { return val_ == a.val_; }
constexpr bool operator!=(const modint &a) const { return val_ != a.val_; }
constexpr auto &operator++() {
*this += 1;
return *this;
}
constexpr auto &operator--() {
*this -= 1;
return *this;
}
constexpr auto operator++(int) {
auto t = *this;
*this += 1;
return t;
}
constexpr auto operator--(int) {
auto t = *this;
*this -= 1;
return t;
}
constexpr static modint pow(int64_t n, int64_t p) {
if (p < 0) return pow(n, -p).inv();
int64_t ret = 1, e = n % M;
for (; p; (e *= e) %= M, p >>= 1)
if (p & 1) (ret *= e) %= M;
return ret;
}
constexpr static modint inv(int64_t a) {
int64_t b = M, u = 1, v = 0;
while (b) {
int64_t t = a / b;
a -= t * b;
std::swap(a, b);
u -= t * v;
std::swap(u, v);
}
u %= M;
if (u < 0) u += M;
return u;
}
constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); }
constexpr auto pow(int64_t p) const { return pow(val_, p); }
constexpr auto inv() const { return inv(val_); }
friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); }
friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; }
friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; }
friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; }
friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; }
friend std::istream &operator>>(std::istream &s, modint &a) {
s >> a.val_;
return s;
}
friend std::ostream &operator<<(std::ostream &s, const modint &a) {
s << a.val_;
return s;
}
template <int N>
static auto div() {
static auto value = inv(N);
return value;
}
explicit operator int32_t() const noexcept { return val_; }
explicit operator int64_t() const noexcept { return val_; }
};
} // namespace haar_lib
#line 11 "test/yukicoder/510/main.test.cpp"
namespace hl = haar_lib;
using mint = hl::modint<1000000007>;
using Mat = hl::square_matrix_const<mint, 4>;
using Monoid = hl::dual_monoid<hl::product_matrix_monoid<Mat>>;
auto f(mint x, mint y) {
Mat ret = {
{1, 0, x, 0},
{0, y, 0, 1},
{0, 2 * y, y * y, 1},
{0, 0, 0, 1}};
return ret;
}
int main() {
int n, q;
std::cin >> n >> q;
hl::segment_tree<Monoid> seg(n);
std::vector<mint> x(n), y(n);
for (int i = 0; i < n; ++i) {
seg.set(i, f(x[i], y[i]));
}
for (auto [c, i] : hl::input_tuples<char, int>(q)) {
if (c == 'x') {
int v;
std::cin >> v;
x[i] = v;
seg.set(i, f(x[i], y[i]));
} else if (c == 'y') {
int v;
std::cin >> v;
y[i] = v;
seg.set(i, f(x[i], y[i]));
} else {
auto m = seg.fold(0, i);
auto ans = dot(m[0], Mat::vector_type({1, 1, 1, 1}));
std::cout << ans << "\n";
}
}
return 0;
}