結果
| 問題 |
No.1549 [Cherry 2nd Tune] BANning Tuple
|
| コンテスト | |
| ユーザー |
 rniya
|
| 提出日時 | 2021-06-11 23:53:29 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,001 ms / 4,000 ms |
| コード長 | 21,175 bytes |
| コンパイル時間 | 6,971 ms |
| コンパイル使用メモリ | 232,896 KB |
| 最終ジャッジ日時 | 2025-01-22 07:20:20 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 20 |
ソースコード
#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()
template <typename T> istream& operator>>(istream& is, vector<T>& v) {
for (T& x : v) is >> x;
return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
}
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << '(' << p.first << ',' << p.second << ')';
return os;
}
template <typename T, typename U, typename V> ostream& operator<<(ostream& os, const tuple<T, U, V>& t) {
os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')';
return os;
}
template <typename T, typename U, typename V, typename W> ostream& operator<<(ostream& os, const tuple<T, U, V, W>& t) {
os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
}
return os;
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
cerr << head;
if (sizeof...(Tail) > 0) cerr << ", ";
debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) \
cerr << " "; \
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
cerr << " "; \
debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }
template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
#pragma endregion
/**
* @brief modint
* @docs docs/modulo/modint.md
*/
template <uint32_t mod> class modint {
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
public:
u32 v;
constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}
constexpr u32& value() noexcept { return v; }
constexpr const u32& value() const noexcept { return v; }
constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
constexpr modint& operator+=(const modint& rhs) noexcept {
v += rhs.v;
if (v >= mod) v -= mod;
return *this;
}
constexpr modint& operator-=(const modint& rhs) noexcept {
if (v < rhs.v) v += mod;
v -= rhs.v;
return *this;
}
constexpr modint& operator*=(const modint& rhs) noexcept {
v = (u64)v * rhs.v % mod;
return *this;
}
constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.pow(mod - 2); }
constexpr modint pow(u64 exp) const noexcept {
modint self(*this), res(1);
while (exp > 0) {
if (exp & 1) res *= self;
self *= self;
exp >>= 1;
}
return res;
}
constexpr modint& operator++() noexcept {
if (++v == mod) v = 0;
return *this;
}
constexpr modint& operator--() noexcept {
if (v == 0) v = mod;
return --v, *this;
}
constexpr modint operator++(int) noexcept {
modint t = *this;
return ++*this, t;
}
constexpr modint operator--(int) noexcept {
modint t = *this;
return --*this, t;
}
constexpr modint operator-() const noexcept { return modint(mod - v); }
template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }
template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }
template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }
template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }
constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }
constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }
constexpr bool operator!() const noexcept { return !v; }
friend istream& operator>>(istream& s, modint& rhs) noexcept {
i64 v;
rhs = modint{(s >> v, v)};
return s;
}
friend ostream& operator<<(ostream& s, const modint& rhs) noexcept { return s << rhs.v; }
};
/**
* @brief Number Theoretic Transform
* @docs docs/convolution/NumberTheoreticTransform.md
*/
template <int mod> struct NumberTheoreticTransform {
using Mint = modint<mod>;
vector<Mint> roots;
vector<int> rev;
int base, max_base;
Mint root;
NumberTheoreticTransform() : base(1), rev{0, 1}, roots{Mint(0), Mint(1)} {
int tmp = mod - 1;
for (max_base = 0; tmp % 2 == 0; max_base++) tmp >>= 1;
root = 2;
while (root.pow((mod - 1) >> 1) == 1) root++;
root = root.pow((mod - 1) >> max_base);
}
void ensure_base(int nbase) {
if (nbase <= base) return;
rev.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (nbase - 1));
}
roots.resize(1 << nbase);
for (; base < nbase; base++) {
Mint z = root.pow(1 << (max_base - 1 - base));
for (int i = 1 << (base - 1); i < (1 << base); i++) {
roots[i << 1] = roots[i];
roots[i << 1 | 1] = roots[i] * z;
}
}
}
void ntt(vector<Mint>& a) {
const int n = a.size();
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += (k << 1)) {
for (int j = 0; j < k; j++) {
Mint z = a[i + j + k] * roots[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while ((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz, Mint(0));
b.resize(sz, Mint(0));
ntt(a);
ntt(b);
Mint inv_sz = 1 / Mint(sz);
for (int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
reverse(a.begin() + 1, a.end());
ntt(a);
a.resize(need);
return a;
}
vector<int> multiply(vector<int> a, vector<int> b) {
vector<Mint> A(a.size()), B(b.size());
for (int i = 0; i < a.size(); i++) A[i] = Mint(a[i]);
for (int i = 0; i < b.size(); i++) B[i] = Mint(b[i]);
vector<Mint> C = multiply(A, B);
vector<int> res(C.size());
for (int i = 0; i < C.size(); i++) res[i] = C[i].v;
return res;
}
};
/**
* @brief Formal Power Series
* @docs docs/polynomial/FormalPowerSeries.md
*/
template <typename M> struct FormalPowerSeries : vector<M> {
using vector<M>::vector;
using Poly = FormalPowerSeries;
using MUL = function<Poly(Poly, Poly)>;
static MUL& get_mul() {
static MUL mul = nullptr;
return mul;
}
static void set_mul(MUL f) { get_mul() = f; }
void shrink() {
while (this->size() && this->back() == M(0)) this->pop_back();
}
Poly pre(int deg) const { return Poly(this->begin(), this->begin() + min((int)this->size(), deg)); }
Poly operator+(const M& v) const { return Poly(*this) += v; }
Poly operator+(const Poly& p) const { return Poly(*this) += p; }
Poly operator-(const M& v) const { return Poly(*this) -= v; }
Poly operator-(const Poly& p) const { return Poly(*this) -= p; }
Poly operator*(const M& v) const { return Poly(*this) *= v; }
Poly operator*(const Poly& p) const { return Poly(*this) *= p; }
Poly operator/(const Poly& p) const { return Poly(*this) /= p; }
Poly operator%(const Poly& p) const { return Poly(*this) %= p; }
Poly& operator+=(const M& v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
return *this;
}
Poly& operator+=(const Poly& p) {
if (p.size() > this->size()) this->resize(p.size());
for (int i = 0; i < (int)p.size(); i++) (*this)[i] += p[i];
return *this;
}
Poly& operator-=(const M& v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
return *this;
}
Poly& operator-=(const Poly& p) {
if (p.size() > this->size()) this->resize(p.size());
for (int i = 0; i < (int)p.size(); i++) (*this)[i] -= p[i];
return *this;
}
Poly& operator*=(const M& v) {
for (int i = 0; i < (int)this->size(); i++) (*this)[i] *= v;
return *this;
}
Poly& operator*=(const Poly& p) {
if (this->empty() || p.empty()) {
this->clear();
return *this;
}
assert(get_mul() != nullptr);
return *this = get_mul()(*this, p);
}
Poly& operator/=(const Poly& p) {
if (this->size() < p.size()) {
this->clear();
return *this;
}
int n = this->size() - p.size() - 1;
debug(n);
Poly a = rev().pre(n);
debug(p.size());
return *this = (rev().pre(n) * p.rev().inv(n)).pre(n).rev(n);
}
Poly& operator%=(const Poly& p) { return *this -= *this / p * p; }
Poly operator<<(const int deg) {
Poly res(*this);
res.insert(res.begin(), deg, M(0));
return res;
}
Poly operator>>(const int deg) {
if (this->size() <= deg) return {};
Poly res(*this);
res.erase(res.begin(), res.begin() + deg);
return res;
}
Poly operator-() const {
Poly res(this->size());
for (int i = 0; i < (int)this->size(); i++) res[i] = -(*this)[i];
return res;
}
Poly rev(int deg = -1) const {
Poly res(*this);
if (~deg) res.resize(deg, M(0));
reverse(res.begin(), res.end());
return res;
}
Poly diff() const {
Poly res(max(0, (int)this->size() - 1));
for (int i = 1; i < (int)this->size(); i++) res[i - 1] = (*this)[i] * M(i);
return res;
}
Poly integral() const {
Poly res(this->size() + 1);
res[0] = M(0);
for (int i = 0; i < (int)this->size(); i++) res[i + 1] = (*this)[i] / M(i + 1);
return res;
}
Poly inv(int deg = -1) const {
assert((*this)[0] != M(0));
if (deg < 0) deg = this->size();
Poly res({M(1) / (*this)[0]});
for (int i = 1; i < deg; i <<= 1) {
res = (res + res - res * res * pre(i << 1)).pre(i << 1);
}
return res.pre(deg);
}
Poly log(int deg = -1) const {
assert((*this)[0] == M(1));
if (deg < 0) deg = this->size();
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
Poly sqrt(int deg = -1) const {
assert((*this)[0] == M(1));
if (deg == -1) deg = this->size();
Poly res({M(1)});
M inv2 = M(1) / M(2);
for (int i = 1; i < deg; i <<= 1) {
res = (res + pre(i << 1) * res.inv(i << 1)) * inv2;
}
return res.pre(deg);
}
Poly exp(int deg = -1) {
assert((*this)[0] == M(0));
if (deg < 0) deg = this->size();
Poly res({M(1)});
for (int i = 1; i < deg; i <<= 1) {
res = (res * (pre(i << 1) + M(1) - res.log(i << 1))).pre(i << 1);
}
return res.pre(deg);
}
Poly pow(long long k, int deg = -1) const {
if (deg < 0) deg = this->size();
for (int i = 0; i < (int)this->size(); i++) {
if ((*this)[i] == M(0)) continue;
if (k * i > deg) return Poly(deg, M(0));
M inv = M(1) / (*this)[i];
Poly res = (((*this * inv) >> i).log() * k).exp() * (*this)[i].pow(k);
res = (res << (i * k)).pre(deg);
if ((int)res.size() < deg) res.resize(deg, M(0));
return res;
}
return *this;
}
Poly pow_mod(long long k, const Poly& mod) const {
Poly x(*this), res = {M(1)};
while (k > 0) {
if (k & 1) res = res * x % mod;
x = x * x % mod;
k >>= 1;
}
return res;
}
Poly linear_mul(const M& a, const M& b) {
Poly res(this->size() + 1);
for (int i = 0; i < this->size() + 1; i++) {
res[i] = (i - 1 >= 0 ? (*this)[i - 1] * a : M(0)) + (i < (int)this->size() ? (*this)[i] * b : M(0));
}
return res;
}
Poly linear_div(const M& a, const M& b) {
Poly res(this->size() - 1);
M inv_b = M(1) / b;
for (int i = 0; i + 1 < (int)this->size(); i++) {
res[i] = ((*this)[i] - (i - 1 >= 0 ? res[i - 1] * a : M(0))) * inv_b;
}
return res;
}
Poly sparse_mul(const M& c, const M& d) {
Poly res(*this);
res.resize(this->size() + d, M(0));
for (int i = 0; i < (int)this->size(); i++) {
res[i + d] += (*this)[i] * c;
}
return res;
}
Poly sparse_div(const M& c, const M& d) {
Poly res(*this);
for (int i = 0; i < res.size() - d; i++) {
res[i + d] -= res[i] * c;
}
return res;
}
M operator()(const M& x) const {
M res = 0, power = 1;
for (int i = 0; i < (int)this->size(); i++, power *= x) {
res += (*this)[i] * power;
}
return res;
}
};
/**
* @brief compress
*/
template <typename T> map<T, int> compress(vector<T>& v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
map<T, int> res;
for (int i = 0; i < v.size(); i++) res[v[i]] = i;
return res;
}
/**
* @brief Segment Tree
* @docs docs/datastructure/SegmentTree.md
*/
template <typename Monoid> struct SegmentTree {
typedef function<Monoid(Monoid, Monoid)> F;
int n;
F f;
Monoid id;
vector<Monoid> dat;
SegmentTree(int n_, F f, Monoid id) : f(f), id(id) { init(n_); }
void init(int n_) {
n = 1;
while (n < n_) n <<= 1;
dat.assign(n << 1, id);
}
void build(const vector<Monoid>& v) {
for (int i = 0; i < (int)v.size(); i++) dat[i + n] = v[i];
for (int i = n - 1; i; i--) dat[i] = f(dat[i << 1 | 0], dat[i << 1 | 1]);
}
void update(int k, Monoid x) {
dat[k += n] = x;
while (k >>= 1) dat[k] = f(dat[k << 1 | 0], dat[k << 1 | 1]);
}
Monoid query(int a, int b) {
if (a >= b) return id;
Monoid vl = id, vr = id;
for (int l = a + n, r = b + n; l < r; l >>= 1, r >>= 1) {
if (l & 1) vl = f(vl, dat[l++]);
if (r & 1) vr = f(dat[--r], vr);
}
return f(vl, vr);
}
template <typename C> int find_subtree(int k, const C& check, Monoid& M, bool type) {
while (k < n) {
Monoid nxt = type ? f(dat[k << 1 | type], M) : f(M, dat[k << 1 | type]);
if (check(nxt))
k = k << 1 | type;
else
M = nxt, k = k << 1 | (type ^ 1);
}
return k - n;
}
// min i s.t. f(seg[a],seg[a+1],...,seg[i]) satisfy "check"
template <typename C> int find_first(int a, const C& check) {
Monoid L = id;
if (a <= 0) {
if (check(f(L, dat[1]))) return find_subtree(1, check, L, false);
return -1;
}
int b = n;
for (int l = a + n, r = b + n; l < r; l >>= 1, r >>= 1) {
if (l & 1) {
Monoid nxt = f(L, dat[l]);
if (check(nxt)) return find_subtree(l, check, L, false);
L = nxt;
l++;
}
}
return -1;
}
// max i s.t. f(seg[i],...,seg[b-2],seg[b-1]) satisfy "check"
template <typename C> int find_last(int b, const C& check) {
Monoid R = id;
if (b >= n) {
if (check(f(dat[1], R))) return find_subtree(1, check, R, true);
return -1;
}
int a = n;
for (int l = a, r = b + n; l < r; l >>= 1, r >>= 1) {
if (r & 1) {
Monoid nxt = f(dat[--r], R);
if (check(nxt)) return find_subtree(r, check, R, true);
R = nxt;
}
}
return -1;
}
Monoid operator[](int i) { return dat[i + n]; }
};
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
// const long long MOD = 1000000007;
const long long MOD = 998244353;
using mint = modint<MOD>;
using FPS = FormalPowerSeries<mint>;
const int MAX_N = 3010;
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
NumberTheoreticTransform<MOD> NTT;
auto mul = [&](const FPS::Poly& a, const FPS::Poly& b) {
auto res = NTT.multiply(a, b);
return FPS::Poly(res.begin(), res.begin() + min((int)res.size(), MAX_N));
};
FPS::set_mul(mul);
ll N;
int Q;
cin >> N >> Q;
vector<ll> K(Q);
vector<int> A(Q), B(Q), S(Q), T(Q);
for (int i = 0; i < Q; i++) cin >> K[i] >> A[i] >> B[i] >> S[i] >> T[i], --K[i];
vector<ll> comp = K;
map<ll, int> mp = compress(comp);
for (ll& x : K) x = mp[x];
int sz = mp.size();
vector<vector<mint>> comb(sz + 1, vector<mint>(MAX_N)); // 和 j を N - i 要素に分割
for (int i = 0; i <= sz; i++) {
ll cur = N - i - 1;
if (i == N) {
comb[i][0] = 1;
continue;
}
comb[i][0] = 1;
for (int j = 1; j < MAX_N; j++) comb[i][j] = comb[i][j - 1] * (++cur) / j;
}
vector<FPS> a(sz, FPS(MAX_N, 1));
FPS id(1, 1);
auto f = [](FPS a, FPS b) -> FPS {
auto c = a * b;
return c;
};
SegmentTree<FPS> seg(sz, f, id);
seg.build(a);
FPS other(MAX_N, 0);
for (int i = 0; i < MAX_N; i++) other[i] = comb[sz][i];
// for (int j = 0; j < 10; j++) cerr << other[j] << (j + 1 == 10 ? '\n' : ' ');
for (int i = 0; i < Q; i++) {
for (int j = A[i]; j <= B[i]; j++) a[K[i]][j] = 0;
seg.update(K[i], a[K[i]]);
auto res = seg.query(0, sz);
// for (int j = 0; j < 10; j++) cerr << res[j] << (j + 1 == 10 ? '\n' : ' ');
res *= other;
// for (int j = 0; j < 10; j++) cerr << res[j] << (j + 1 == 10 ? '\n' : ' ');
mint ans = 0;
for (int j = S[i]; j <= min((int)res.size() - 1, T[i]); j++) ans += res[j];
cout << ans << '\n';
}
return 0;
}