結果

問題 No.2575 Almost Increasing Sequence
ユーザー Forested
提出日時 2023-12-03 15:24:55
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 11,279 bytes
コンパイル時間 1,677 ms
コンパイル使用メモリ 136,176 KB
実行使用メモリ 6,676 KB
スコア 0
最終ジャッジ日時 2023-12-03 15:27:30
合計ジャッジ時間 154,704 ms
ジャッジサーバーID
(参考情報)
judge12 / judge11
このコードへのチャレンジ
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ファイルパターン 結果
sample WA * 1
other WA * 19
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ソースコード

diff #
プレゼンテーションモードにする

#ifndef LOCAL
#define FAST_IO
#endif
// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
template <typename T>
using Vec = vector<T>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
istream &operator>>(istream &is, i128 &x) {
i64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, i128 x) {
os << (i64)x;
return os;
}
istream &operator>>(istream &is, u128 &x) {
u64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, u128 x) {
os << (u64)x;
return os;
}
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
// ============
#ifdef DEBUGF
#else
#define DBG(x) (void) 0
#endif
// ============
#include <cassert>
#include <iostream>
#include <type_traits>
// ============
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = (unsigned) ((unsigned long long) ret * self % mod);
}
self = (unsigned) ((unsigned long long) self * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok)
return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
// ============
template <unsigned mod>
class ModInt {
static_assert(mod != 0, "`mod` must not be equal to 0.");
static_assert(
mod < (1u << 31),
"`mod` must be less than (1u << 31) = 2147483648.");
unsigned val;
public:
static constexpr unsigned get_mod() {
return mod;
}
constexpr ModInt() : val(0) {}
template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned) (x % mod)) {}
static constexpr ModInt raw(unsigned x) {
ModInt<mod> ret;
ret.val = x;
return ret;
}
constexpr unsigned get_val() const {
return val;
}
constexpr ModInt operator+() const {
return *this;
}
constexpr ModInt operator-() const {
return ModInt<mod>(0u) - *this;
}
constexpr ModInt &operator+=(const ModInt &rhs) {
val += rhs.val;
if (val >= mod)
val -= mod;
return *this;
}
constexpr ModInt &operator-=(const ModInt &rhs) {
val -= rhs.val;
if (val >= mod)
val += mod;
return *this;
}
constexpr ModInt &operator*=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.val % mod;
return *this;
}
constexpr ModInt &operator/=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.inv().val % mod;
return *this;
}
friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) += rhs;
}
friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) -= rhs;
}
friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) *= rhs;
}
friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) /= rhs;
}
constexpr ModInt pow(unsigned long long x) const {
ModInt<mod> ret = ModInt<mod>::raw(1);
ModInt<mod> self = *this;
while (x != 0) {
if (x & 1)
ret *= self;
self *= self;
x >>= 1;
}
return ret;
}
constexpr ModInt inv() const {
static_assert(is_prime(mod), "`mod` must be a prime number.");
assert(val != 0);
return this->pow(mod - 2);
}
friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
long long val;
is >> val;
x.val = val % mod + (val < 0 ? mod : 0);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
os << x.val;
return os;
}
friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
return lhs.val != rhs.val;
}
};
[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;
// ============
// ============
#include <vector>
#include <cassert>
template <typename T>
class FactorialTable {
std::vector<T> fac;
std::vector<T> ifac;
public:
FactorialTable() : fac(1, T(1)), ifac(1, T(1)) {}
FactorialTable(int n) : fac(n + 1), ifac(n + 1) {
assert(n >= 0);
fac[0] = T(1);
for (int i = 1; i <= n; ++i) {
fac[i] = fac[i - 1] * T(i);
}
ifac[n] = T(1) / T(fac[n]);
for (int i = n; i > 0; --i) {
ifac[i - 1] = ifac[i] * T(i);
}
}
void resize(int n) {
int old = n_max();
if (n <= old) {
return;
}
fac.resize(n + 1);
for (int i = old + 1; i <= n; ++i) {
fac[i] = fac[i - 1] * T(i);
}
ifac.resize(n + 1);
ifac[n] = T(1) / T(fac[n]);
for (int i = n; i > old; --i) {
ifac[i - 1] = ifac[i] * T(i);
}
}
inline int n_max() const {
return (int) fac.size() - 1;
}
inline T fact(int n) const {
assert(n >= 0 && n <= n_max());
return fac[n];
}
inline T inv_fact(int n) const {
assert(n >= 0 && n <= n_max());
return ifac[n];
}
inline T inv_n(int n) const {
assert(n > 0 && n <= n_max());
return ifac[n] * fac[n - 1];
}
inline T choose(int n, int k) const {
assert(k <= n_max() && n <= n_max());
if (k > n || k < 0) {
return T(0);
}
return fac[n] * ifac[k] * ifac[n - k];
}
inline T multi_choose(int n, int k) const {
assert(n >= 1 && k >= 0 && k + n - 1 <= n_max());
return choose(k + n - 1, k);
}
inline T n_terms_sum_k(int n, int k) const {
assert(n >= 0);
if (k < 0) {
return T(0);
}
if (n == 0) {
return k == 0 ? T(1) : T(0);
}
return choose(n + k - 1, n - 1);
}
};
// ============
using M = ModInt<998244353>;
int main() {
i32 k;
cin >> k;
i32 n = 20000;
Vec<M> pwk(n + 1);
REP(i, n + 1) {
pwk[i] = M(i).pow(k);
}
FactorialTable<M> table(n + 2);
Vec<M> s0(n + 1), s1(n + 1), s2(n + 1), s3(n + 1), s4(n + 1);
Vec<M> ans(n + 1);
REP(a_, 1, n + 1) {
M a(a_);
M a2 = a * a;
M a3 = a2 * a;
M a4 = a3 * a;
if (a_ >= 3) {
REP(i, a_, n + 1) {
i32 rem = i + 3 - a_;
M coeff = pwk[a_ - 2] * table.fact(i) * table.fact(i) * table.inv_fact(a_) * table.inv_fact(a_);
M sum;
sum += s0[rem];
sum += a * s1[rem];
sum += a2 * s2[rem];
sum += a3 * s3[rem];
sum += a4 * s4[rem];
ans[i] += coeff * sum;
}
}
if (a_ >= 2) {
i32 b_ = a_;
M b(b_);
M b2 = b * b;
M b3 = b2 * b;
M b4 = b3 * b;
REP(c_, 1, b_) {
if (b_ + c_ >= n + 1) {
break;
}
M c(c_);
M c2 = c * c;
M c3 = c2 * c;
M c4 = c3 * c;
i32 idx = b_ + c_;
M coeff = table.inv_fact(b_) * table.inv_fact(b_) * table.inv_fact(c_) * table.inv_fact(c_);
s0[idx] += coeff * (b4 * c2 - M(2) * b3 * c3 + b2 * c4);
s1[idx] += coeff * M(2) * (-b4 * c + b3 * c2 + b2 * c3 - b * c4);
s2[idx] += coeff * (b4 + M(2) * b3 * c - M(6) * b2 * c2 + M(2) * b * c3 + c4);
s3[idx] += coeff * M(2) * (-b3 + b2 * c + b * c2 - c3);
s4[idx] += coeff * (b2 - M(2) * b * c + c2);
}
}
}
REP(i, 1, n + 1) {
cout << ans[i] << " \n"[i == n];
}
}
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