#line 1 "test/yj_range_affine_range_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#include <cstdint>
#include <cstdio>
#include <vector>
#line 1 "DataStructure/segment_tree.cpp"
/**
* @brief 区間作用・区間和セグメント木
* @author えびちゃん
*/
#include <cstddef>
#line 11 "DataStructure/segment_tree.cpp"
#line 1 "integer/bit.cpp"
/**
* @brief ビット演算
* @author えびちゃん
*/
// XXX integral promotion 関連の注意をあまりしていません
#include <climits>
#include <type_traits>
template <typename Tp>
constexpr auto countl_zero(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
int bits = (sizeof(value_type) * CHAR_BIT);
if (n == 0) return bits;
int res = 0;
for (int i = bits / 2; i > 0; i /= 2) {
value_type mask = ((static_cast<value_type>(1) << i) - 1) << i;
if (n & mask) n >>= i;
else res += i;
}
return res;
}
template <typename Tp>
constexpr auto countl_one(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
return countl_zero(static_cast<value_type>(~n));
}
template <typename Tp>
constexpr auto countr_zero(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
int bits = (sizeof(value_type) * CHAR_BIT);
if (n == 0) return bits;
int res = 0;
for (int i = bits / 2; i > 0; i /= 2) {
value_type mask = ((static_cast<value_type>(1) << i) - 1);
if (!(n & mask)) res += i, n >>= i;
}
return res;
}
template <typename Tp>
constexpr auto countr_one(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
return countr_zero(static_cast<value_type>(~n));
}
constexpr unsigned long long half_mask[] = {
0x5555555555555555uLL, 0x3333333333333333uLL, 0x0F0F0F0F0F0F0F0FuLL,
0x00FF00FF00FF00FFuLL, 0x0000FFFF0000FFFFuLL, 0x00000000FFFFFFFFuLL
};
template <typename Tp>
constexpr auto popcount(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
int bits = static_cast<int>((sizeof n) * CHAR_BIT);
for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
if (j <= 8) n = (n & half_mask[i]) + ((n >> j) & half_mask[i]);
else n += n >> j;
}
return n & 0xFF;
}
template <typename Tp>
constexpr auto parity(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{ return popcount(n) & 1; }
template <typename Tp>
int clz(Tp n) { return countl_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }
template <typename Tp>
int ctz(Tp n) { return countr_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }
template <typename Tp>
int ilog2(Tp n) {
return (CHAR_BIT * sizeof(Tp) - 1) - clz(static_cast<typename std::make_unsigned<Tp>::type>(n));
}
template <typename Tp>
bool is_pow2(Tp n) { return (n > 0) && ((n & (n-1)) == 0); }
template <typename Tp>
Tp floor2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(1) << ilog2(n); }
template <typename Tp>
Tp ceil2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(2) << ilog2(n); }
template <typename Tp>
constexpr auto reverse(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, Tp>::type
{
int bits = static_cast<int>((sizeof n) * CHAR_BIT);
for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
n = ((n & half_mask[i]) << j) | ((n >> j) & half_mask[i]);
}
return n;
}
#line 13 "DataStructure/segment_tree.cpp"
template <typename Operation>
class segment_tree {
public:
using size_type = size_t;
using operation = Operation;
using operand_type = typename operation::operand_type;
using action_type = typename operation::action_type;
using value_type = operand_type;
private:
size_type M_n;
std::vector<operand_type> M_c;
std::vector<action_type> M_d; // deferred
void M_build(size_type i) {
while (i > 1) {
i >>= 1;
M_c[i] = (M_c[i<<1|0] + M_c[i<<1|1]);
operation::act(M_c[i], M_d[i]);
}
}
void M_resolve(size_type i) {
size_type h = ilog2(M_n) + 2; // ilog2p1(M_n*2)
for (size_type s = h; s > 0; --s) {
size_type p = i >> s;
action_type id{};
if (M_d[p] != id) {
M_apply(p<<1|0, M_d[p]);
M_apply(p<<1|1, M_d[p]);
M_d[p] = id;
}
}
}
void M_apply(size_type i, action_type const& x) {
operation::act(M_c[i], x);
if (i < M_n) M_d[i] += x;
}
public:
segment_tree() = default;
explicit segment_tree(size_type n):
M_n(n), M_c(n+n, operand_type{}), M_d(n, action_type{}) {}
segment_tree(size_type n, operand_type const& x):
M_n(n), M_c(n+n, x), M_d(n, action_type{})
{
for (size_type i = n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
template <typename InputIt>
segment_tree(InputIt first, InputIt last): M_c(first, last) {
M_n = M_c.size();
M_d.assign(M_n, action_type{});
M_c.insert(M_c.begin(), M_n, operand_type{});
for (size_type i = M_n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
void assign(size_type n) {
M_n = n;
M_c(n+n, operand_type{});
M_d(n, action_type{});
}
void assign(size_type n, operand_type const& x) {
M_n = n;
M_c(n+n, x);
M_d(n, action_type{});
for (size_type i = n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
template <typename InputIt>
void assign(InputIt first, InputIt last) {
M_c.assign(first, last);
M_n = M_c.size();
M_d.assign(M_n, action_type{});
M_c.insert(M_c.begin(), M_n, operand_type{});
for (size_type i = M_n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
void act(size_type l, size_type r, action_type const& x) {
if (l == r) return;
l += M_n;
r += M_n;
size_type l0 = l;
size_type r0 = r;
M_resolve(l0);
M_resolve(r0-1);
while (l < r) {
if (l & 1) M_apply(l++, x);
if (r & 1) M_apply(--r, x);
l >>= 1;
r >>= 1;
}
M_build(l0);
M_build(r0-1);
}
operand_type fold(size_type l, size_type r) {
operand_type resl{}, resr{};
if (l == r) return resl;
l += M_n;
r += M_n;
M_resolve(l);
M_resolve(r-1);
while (l < r) {
if (l & 1) resl += M_c[l++];
if (r & 1) resr = M_c[--r] + std::move(resr);
l >>= 1;
r >>= 1;
}
return resl += resr;
}
operand_type operator [](size_type i) {
i += M_n;
M_resolve(i);
return M_c[i];
}
};
#line 1 "utility/action/affine_sum.cpp"
/**
* @brief 区間 Affine 変換・区間加算用のヘルパークラス
* @author えびちゃん
*/
#line 1 "utility/monoid/composite.cpp"
/**
* @brief 一次関数の合成を得る演算のモノイド
* @author えびちゃん
*/
#include <algorithm>
#include <utility>
#ifndef H_composite_monoid
#define H_composite_monoid
template <typename Tp>
class composite_monoid {
public:
using value_type = Tp;
private:
value_type M_a = 1;
value_type M_b = 0;
public:
composite_monoid() = default; // identity
composite_monoid(value_type a, value_type b): M_a(a), M_b(b) {};
composite_monoid& operator +=(composite_monoid that) {
M_a *= that.M_a;
M_b *= that.M_a;
M_b += that.M_b;
return *this;
}
composite_monoid operator +(composite_monoid const& that) const {
return composite_monoid(*this) += that;
}
composite_monoid operator +(composite_monoid&& that) const {
return composite_monoid(*this) += std::move(that);
}
bool operator ==(composite_monoid const& that) const {
return (M_a == that.M_a && M_b == that.M_b);
}
bool operator !=(composite_monoid const& that) const { return !(*this == that); }
auto get() const { return std::make_pair(M_a, M_b); }
value_type operator ()(value_type x) const { return M_a * x + M_b; }
};
#endif /* !defined(H_composite_monoid) */
#line 1 "utility/monoid/length.cpp"
/**
* @brief 和と長さを得る演算のモノイド
* @author えびちゃん
*/
#line 8 "utility/monoid/length.cpp"
#ifndef H_length_monoid
#define H_length_monoid
template <typename Tp>
class length_monoid {
public:
using value_type = Tp;
using size_type = size_t;
private:
value_type M_x{};
size_type M_l = 1;
public:
length_monoid() = default; // identity
length_monoid(value_type const& x, size_type l = 1): M_x(x), M_l(l) {};
length_monoid(value_type&& x, size_type l = 1): M_x(std::move(x)), M_l(l) {};
length_monoid& operator +=(length_monoid const& that) {
M_x += that.M_x;
M_l += that.M_l;
return *this;
}
length_monoid& operator +=(length_monoid&& that) {
M_x += std::move(that.M_x);
M_l += that.M_l;
return *this;
}
length_monoid operator +(length_monoid const& that) const {
return length_monoid(*this) += that;
}
length_monoid operator +(length_monoid&& that) const {
return length_monoid(*this) += std::move(that);
}
value_type const& get() const { return M_x; }
size_type length() const { return M_l; }
};
#endif /* !defined(H_length_monoid) */
#line 11 "utility/action/affine_sum.cpp"
#line 13 "utility/action/affine_sum.cpp"
template <typename Tp>
struct action_affine_to_sum {
using operand_type = length_monoid<Tp>;
using action_type = composite_monoid<Tp>;
static void act(operand_type& op, action_type const& f) {
auto [a, b] = f.get();
op = operand_type(a * op.get() + op.length() * b, op.length());
}
};
#line 1 "ModularArithmetic/modint.cpp"
/**
* @brief 合同算術用クラス
* @author えびちゃん
*/
#line 10 "ModularArithmetic/modint.cpp"
#include <limits>
#include <type_traits>
#line 13 "ModularArithmetic/modint.cpp"
template <intmax_t Modulo>
class modint {
public:
using value_type = typename std::conditional<
(0 < Modulo && Modulo < std::numeric_limits<int>::max() / 2), int, intmax_t
>::type;
private:
static constexpr value_type S_cmod = Modulo; // compile-time
static value_type S_rmod; // runtime
value_type M_value = 0;
static constexpr value_type S_inv(value_type n, value_type m) {
value_type x = 0;
value_type y = 1;
value_type a = n;
value_type b = m;
for (value_type u = y, v = x; a;) {
value_type q = b / a;
std::swap(x -= q*u, u);
std::swap(y -= q*v, v);
std::swap(b -= q*a, a);
}
if ((x %= m) < 0) x += m;
return x;
}
static value_type S_normalize(intmax_t n, value_type m) {
if (n >= m) {
n %= m;
} else if (n < 0) {
if ((n %= m) < 0) n += m;
}
return n;
}
public:
modint() = default;
modint(intmax_t n): M_value(S_normalize(n, get_modulo())) {}
modint& operator =(intmax_t n) {
M_value = S_normalize(n, get_modulo());
return *this;
}
modint& operator +=(modint const& that) {
if ((M_value += that.M_value) >= get_modulo()) M_value -= get_modulo();
return *this;
}
modint& operator -=(modint const& that) {
if ((M_value -= that.M_value) < 0) M_value += get_modulo();
return *this;
}
modint& operator *=(modint const& that) {
intmax_t tmp = M_value;
tmp *= that.M_value;
M_value = tmp % get_modulo();
return *this;
}
modint& operator /=(modint const& that) {
intmax_t tmp = M_value;
tmp *= S_inv(that.M_value, get_modulo());
M_value = tmp % get_modulo();
return *this;
}
modint& operator ++() {
if (++M_value == get_modulo()) M_value = 0;
return *this;
}
modint& operator --() {
if (M_value-- == 0) M_value = get_modulo()-1;
return *this;
}
modint operator ++(int) { modint tmp(*this); ++*this; return tmp; }
modint operator --(int) { modint tmp(*this); --*this; return tmp; }
friend modint operator +(modint lhs, modint const& rhs) { return lhs += rhs; }
friend modint operator -(modint lhs, modint const& rhs) { return lhs -= rhs; }
friend modint operator *(modint lhs, modint const& rhs) { return lhs *= rhs; }
friend modint operator /(modint lhs, modint const& rhs) { return lhs /= rhs; }
modint operator +() const { return *this; }
modint operator -() const {
if (M_value == 0) return *this;
return modint(get_modulo() - M_value);
}
friend bool operator ==(modint const& lhs, modint const& rhs) {
return lhs.M_value == rhs.M_value;
}
friend bool operator !=(modint const& lhs, modint const& rhs) {
return !(lhs == rhs);
}
value_type get() const { return M_value; }
static value_type get_modulo() { return ((S_cmod > 0)? S_cmod: S_rmod); }
template <int M = Modulo, typename Tp = typename std::enable_if<(M <= 0)>::type>
static Tp set_modulo(value_type m) { S_rmod = m; }
};
template <intmax_t N>
constexpr typename modint<N>::value_type modint<N>::S_cmod;
template <intmax_t N>
typename modint<N>::value_type modint<N>::S_rmod;
#line 10 "test/yj_range_affine_range_sum.test.cpp"
constexpr intmax_t mod = 998244353;
using mi = modint<mod>;
int main() {
size_t n, q;
scanf("%zu %zu", &n, &q);
std::vector<intmax_t> a(n);
for (auto& ai: a) scanf("%jd", &ai);
segment_tree<action_affine_to_sum<mi>> st(a.begin(), a.end());
for (size_t i = 0; i < q; ++i) {
int t;
scanf("%d", &t);
if (t == 0) {
size_t l, r;
int b, c;
scanf("%zu %zu %d %d", &l, &r, &b, &c);
st.act(l, r, {b, c});
} else if (t == 1) {
size_t l, r;
scanf("%zu %zu", &l, &r);
printf("%d\n", st.fold(l, r).get().get());
}
}
}
test/yj_range_affine_range_sum.test.cpp