結果
| 問題 | No.1145 Sums of Powers |
| ユーザー |
 kuhaku
|
| 提出日時 | 2024-05-09 13:18:27 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 316 ms / 2,000 ms |
| コード長 | 35,924 bytes |
| コンパイル時間 | 6,939 ms |
| コンパイル使用メモリ | 312,280 KB |
| 実行使用メモリ | 8,284 KB |
| 最終ジャッジ日時 | 2024-05-09 13:18:37 |
| 合計ジャッジ時間 | 8,519 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 4 ms
5,376 KB |
| testcase_03 | AC | 315 ms
7,820 KB |
| testcase_04 | AC | 311 ms
8,284 KB |
| testcase_05 | AC | 316 ms
7,800 KB |
ソースコード
#line 1 "a.cpp"
#define PROBLEM ""
#line 1 "/home/kuhaku/atcoder/github/algo/lib/fft/ntt.hpp"
#include <algorithm>
#include <cassert>
#include <type_traits>
#include <vector>
#line 2 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_fft.hpp"
#include <array>
#line 4 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_fft.hpp"
#include <cstdint>
#line 2 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_bit.hpp"
namespace internal {
// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
unsigned int x = 1;
while (x < (unsigned int)(n)) x *= 2;
return x;
}
// @param n `1 <= n`
// @return same with std::bit::countl_zero
int countl_zero(unsigned int n) { return __builtin_clz(n); }
// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) { return __builtin_ctz(n); }
// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
} // namespace internal
#line 3 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_math.hpp"
#include <utility>
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr std::int64_t safe_mod(std::int64_t x, std::int64_t m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
std::uint64_t im;
// @param m `1 <= m`
explicit barrett(unsigned int m) : _m(m), im((std::uint64_t)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
std::uint64_t z = a;
z *= b;
std::uint64_t x = (std::uint64_t)(((__uint128_t)(z)*im) >> 64);
std::uint64_t y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
struct montgomery {
std::uint64_t _m;
std::uint64_t im;
std::uint64_t r2;
// @param m `1 <= m`
explicit constexpr montgomery(std::uint64_t m) : _m(m), im(m), r2(-__uint128_t(m) % m) {
for (int i = 0; i < 5; ++i) im = im * (2 - _m * im);
im = -im;
}
// @return m
constexpr std::uint64_t umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
constexpr std::uint64_t mul(std::uint64_t a, std::uint64_t b) const { return mr(mr(a, b), r2); }
constexpr std::uint64_t exp(std::uint64_t a, std::uint64_t b) const {
std::uint64_t res = 1, p = mr(a, r2);
while (b) {
if (b & 1) res = mr(res, p);
p = mr(p, p);
b >>= 1;
}
return res;
}
constexpr bool same_pow(std::uint64_t x, int s, std::uint64_t n) const {
x = mr(x, r2), n = mr(n, r2);
for (int r = 0; r < s; r++) {
if (x == n) return true;
x = mr(x, x);
}
return false;
}
private:
constexpr std::uint64_t mr(std::uint64_t x) const {
return ((__uint128_t)(x * im) * _m + x) >> 64;
}
constexpr std::uint64_t mr(std::uint64_t a, std::uint64_t b) const {
__uint128_t t = (__uint128_t)a * b;
std::uint64_t inc = std::uint64_t(t) != 0;
std::uint64_t x = t >> 64, y = ((__uint128_t)(a * b * im) * _m) >> 64;
unsigned long long z = 0;
bool f = __builtin_uaddll_overflow(x, y, &z);
z += inc;
return f ? z - _m : z;
}
};
constexpr bool is_SPRP32(std::uint32_t n, std::uint32_t a) {
std::uint32_t d = n - 1, s = 0;
while ((d & 1) == 0) ++s, d >>= 1;
std::uint64_t cur = 1, pw = d;
while (pw) {
if (pw & 1) cur = (cur * a) % n;
a = (std::uint64_t)a * a % n;
pw >>= 1;
}
if (cur == 1) return true;
for (std::uint32_t r = 0; r < s; r++) {
if (cur == n - 1) return true;
cur = cur * cur % n;
}
return false;
}
// given 2 <= n,a < 2^64, a prime, check whether n is a-SPRP
constexpr bool is_SPRP64(const montgomery &m, std::uint64_t a) {
auto n = m.umod();
if (n == a) return true;
if (n % a == 0) return false;
std::uint64_t d = n - 1;
int s = 0;
while ((d & 1) == 0) ++s, d >>= 1;
std::uint64_t cur = m.exp(a, d);
if (cur == 1) return true;
return m.same_pow(cur, s, n - 1);
}
constexpr bool is_prime_constexpr(std::uint64_t x) {
if (x == 2 || x == 3 || x == 5 || x == 7) return true;
if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
if (x < 121) return (x > 1);
montgomery m(x);
constexpr std::uint64_t bases[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
for (auto a : bases) {
if (!is_SPRP64(m, a)) return false;
}
return true;
}
constexpr bool is_prime_constexpr(std::int64_t x) {
if (x < 0) return false;
return is_prime_constexpr(std::uint64_t(x));
}
constexpr bool is_prime_constexpr(std::uint32_t x) {
if (x == 2 || x == 3 || x == 5 || x == 7) return true;
if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
if (x < 121) return (x > 1);
std::uint64_t h = x;
h = ((h >> 16) ^ h) * 0x45d9f3b;
h = ((h >> 16) ^ h) * 0x45d9f3b;
h = ((h >> 16) ^ h) & 255;
constexpr uint16_t bases[] = {
15591, 2018, 166, 7429, 8064, 16045, 10503, 4399, 1949, 1295, 2776, 3620, 560,
3128, 5212, 2657, 2300, 2021, 4652, 1471, 9336, 4018, 2398, 20462, 10277, 8028,
2213, 6219, 620, 3763, 4852, 5012, 3185, 1333, 6227, 5298, 1074, 2391, 5113,
7061, 803, 1269, 3875, 422, 751, 580, 4729, 10239, 746, 2951, 556, 2206,
3778, 481, 1522, 3476, 481, 2487, 3266, 5633, 488, 3373, 6441, 3344, 17,
15105, 1490, 4154, 2036, 1882, 1813, 467, 3307, 14042, 6371, 658, 1005, 903,
737, 1887, 7447, 1888, 2848, 1784, 7559, 3400, 951, 13969, 4304, 177, 41,
19875, 3110, 13221, 8726, 571, 7043, 6943, 1199, 352, 6435, 165, 1169, 3315,
978, 233, 3003, 2562, 2994, 10587, 10030, 2377, 1902, 5354, 4447, 1555, 263,
27027, 2283, 305, 669, 1912, 601, 6186, 429, 1930, 14873, 1784, 1661, 524,
3577, 236, 2360, 6146, 2850, 55637, 1753, 4178, 8466, 222, 2579, 2743, 2031,
2226, 2276, 374, 2132, 813, 23788, 1610, 4422, 5159, 1725, 3597, 3366, 14336,
579, 165, 1375, 10018, 12616, 9816, 1371, 536, 1867, 10864, 857, 2206, 5788,
434, 8085, 17618, 727, 3639, 1595, 4944, 2129, 2029, 8195, 8344, 6232, 9183,
8126, 1870, 3296, 7455, 8947, 25017, 541, 19115, 368, 566, 5674, 411, 522,
1027, 8215, 2050, 6544, 10049, 614, 774, 2333, 3007, 35201, 4706, 1152, 1785,
1028, 1540, 3743, 493, 4474, 2521, 26845, 8354, 864, 18915, 5465, 2447, 42,
4511, 1660, 166, 1249, 6259, 2553, 304, 272, 7286, 73, 6554, 899, 2816,
5197, 13330, 7054, 2818, 3199, 811, 922, 350, 7514, 4452, 3449, 2663, 4708,
418, 1621, 1171, 3471, 88, 11345, 412, 1559, 194};
return is_SPRP32(x, bases[h]);
}
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr std::int64_t pow_mod_constexpr(std::int64_t x, std::int64_t n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
std::uint64_t r = 1;
std::uint64_t y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
std::int64_t d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr std::int64_t bases[3] = {2, 7, 61};
for (std::int64_t a : bases) {
std::int64_t t = d;
std::int64_t y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) { return false; }
}
return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<std::int64_t, std::int64_t> inv_gcd(std::int64_t a, std::int64_t b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
std::int64_t s = b, t = a;
std::int64_t m0 = 0, m1 = 1;
while (t) {
std::int64_t u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (std::int64_t)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) { x /= i; }
}
}
if (x > 1) { divs[cnt++] = x; }
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
#line 3 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_type_traits.hpp"
#include <numeric>
#line 5 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_type_traits.hpp"
namespace internal {
template <class T>
using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type, std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;
template <class T>
using is_integral =
typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_signed_int =
typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value, make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
std::common_type<T>>::type>::type;
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
#line 3 "/home/kuhaku/atcoder/github/algo/lib/math/modint.hpp"
#include <iostream>
#line 7 "/home/kuhaku/atcoder/github/algo/lib/math/modint.hpp"
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static constexpr mint raw(int v) {
mint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
constexpr static_modint(T v) : _v(0) {
std::int64_t x = (std::int64_t)(v % (std::int64_t)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
constexpr static_modint(T v) : _v(0) {
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const { return _v; }
constexpr mint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr mint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr mint operator++(int) {
mint result = *this;
++*this;
return result;
}
constexpr mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint &operator+=(const mint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint &operator-=(const mint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint &operator*=(const mint &rhs) {
std::uint64_t z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
constexpr mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(std::int64_t n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend constexpr mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend constexpr mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend constexpr mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend constexpr bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend constexpr bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend std::istream &operator>>(std::istream &is, mint &rhs) {
std::int64_t t;
is >> t;
rhs = mint(t);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
return os << rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id>
struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
dynamic_modint(T v) {
std::int64_t x = (std::int64_t)(v % (std::int64_t)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint &operator+=(const mint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint &operator-=(const mint &rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint &operator*=(const mint &rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(std::int64_t n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend std::istream &operator>>(std::istream &is, mint &rhs) {
std::int64_t t;
is >> t;
rhs = mint(t);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
return os << rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998244353);
using modint998 = static_modint<998244353>;
using modint107 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
#line 11 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_fft.hpp"
namespace internal {
template <class mint, int g = internal::primitive_root<mint::mod()>,
internal::is_static_modint_t<mint> * = nullptr>
struct fft_info {
static constexpr int rank2 = countr_zero_constexpr(mint::mod() - 1);
std::array<mint, rank2 + 1> root, iroot;
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2, irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3, irate3;
fft_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
};
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly(std::vector<mint> &a) {
int n = int(a.size());
int h = internal::countr_zero((unsigned int)n);
static const fft_info<mint> info;
int len = 0;
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
for (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset], r = a[i + offset + p] * rot;
a[i + offset] = l + r, a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len)) rot *= info.rate2[countr_zero(~(unsigned int)(s))];
}
len++;
} else {
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i + offset].val();
auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len)) rot *= info.rate3[countr_zero(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly_inv(std::vector<mint> &a) {
int n = int(a.size());
int h = internal::countr_zero((unsigned int)n);
static const fft_info<mint> info;
int len = h;
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset], r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(std::uint64_t)(mint::mod() + l.val() - r.val()) * irot.val();
;
}
if (s + 1 != (1 << (len - 1))) irot *= info.irate2[countr_zero(~(unsigned int)(s))];
}
len--;
} else {
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].val();
auto a1 = 1ULL * a[i + offset + 1 * p].val();
auto a2 = 1ULL * a[i + offset + 2 * p].val();
auto a3 = 1ULL * a[i + offset + 3 * p].val();
auto a2na3iimag = 1ULL * mint((mint::mod() + a2 - a3) * iimag.val()).val();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] = (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
a[i + offset + 2 * p] =
(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) * irot2.val();
a[i + offset + 3 * p] =
(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) * irot3.val();
}
if (s + 1 != (1 << (len - 2))) irot *= info.irate3[countr_zero(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint> &a, const std::vector<mint> &b) {
int n = int(a.size()), m = int(b.size());
std::vector<mint> ans(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) ans[i + j] += a[i] * b[j];
}
} else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];
}
}
return ans;
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) { a[i] *= b[i]; }
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
} // namespace internal
#line 2 "/home/kuhaku/atcoder/github/algo/lib/template/template.hpp"
#pragma GCC target("sse4.2,avx2,bmi2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
template <class T, class U>
constexpr bool chmax(T &a, const U &b) {
return a < (T)b ? a = (T)b, true : false;
}
template <class T, class U>
constexpr bool chmin(T &a, const U &b) {
return (T)b < a ? a = (T)b, true : false;
}
constexpr std::int64_t INF = 1000000000000000003;
constexpr int Inf = 1000000003;
constexpr double EPS = 1e-7;
constexpr double PI = M_PI;
#line 7 "/home/kuhaku/atcoder/github/algo/lib/fft/ntt.hpp"
/**
* @brief 畳み込み
*
* @tparam mint
* @param a
* @param b
* @return std::vector<mint>
*/
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution(std::vector<mint> &&a, std::vector<mint> &&b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution(const std::vector<mint> &a, const std::vector<mint> &b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <unsigned int mod = 998244353, class T,
std::enable_if_t<std::is_integral<T>::value> * = nullptr>
std::vector<T> convolution(const std::vector<T> &a, const std::vector<T> &b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) { a2[i] = mint(a[i]); }
for (int i = 0; i < m; i++) { b2[i] = mint(b[i]); }
auto c2 = convolution(std::move(a2), std::move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) { c[i] = c2[i].val(); }
return c;
}
std::vector<std::int64_t> convolution_ll(const std::vector<std::int64_t> &a,
const std::vector<std::int64_t> &b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr std::uint64_t MOD1 = 754974721; // 2^24
static constexpr std::uint64_t MOD2 = 167772161; // 2^25
static constexpr std::uint64_t MOD3 = 469762049; // 2^26
static constexpr std::uint64_t M2M3 = MOD2 * MOD3;
static constexpr std::uint64_t M1M3 = MOD1 * MOD3;
static constexpr std::uint64_t M1M2 = MOD1 * MOD2;
static constexpr std::uint64_t M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr std::uint64_t i1 = internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr std::uint64_t i2 = internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr std::uint64_t i3 = internal::inv_gcd(MOD1 * MOD2, MOD3).second;
static constexpr int MAX_AB_BIT = 24;
static_assert(MOD1 % (1ull << MAX_AB_BIT) == 1,
"MOD1 isn't enough to support an array length of 2^24.");
static_assert(MOD2 % (1ull << MAX_AB_BIT) == 1,
"MOD2 isn't enough to support an array length of 2^24.");
static_assert(MOD3 % (1ull << MAX_AB_BIT) == 1,
"MOD3 isn't enough to support an array length of 2^24.");
assert(n + m - 1 <= (1 << MAX_AB_BIT));
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<std::int64_t> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
std::uint64_t x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
std::int64_t diff = c1[i] - internal::safe_mod((std::int64_t)(x), (std::int64_t)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr std::uint64_t offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
#line 3 "/home/kuhaku/atcoder/github/algo/lib/template/macro.hpp"
#define FOR(i, m, n) for (int i = (m); i < int(n); ++i)
#define FORR(i, m, n) for (int i = (m)-1; i >= int(n); --i)
#define FORL(i, m, n) for (int64_t i = (m); i < int64_t(n); ++i)
#define rep(i, n) FOR (i, 0, n)
#define repn(i, n) FOR (i, 1, n + 1)
#define repr(i, n) FORR (i, n, 0)
#define repnr(i, n) FORR (i, n + 1, 1)
#define all(s) (s).begin(), (s).end()
#line 3 "/home/kuhaku/atcoder/github/algo/lib/template/sonic.hpp"
struct Sonic {
Sonic() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(20);
}
constexpr void operator()() const {}
} sonic;
#line 5 "/home/kuhaku/atcoder/github/algo/lib/template/atcoder.hpp"
using namespace std;
using ll = std::int64_t;
using ld = long double;
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
return is >> p.first >> p.second;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for (T &i : v) is >> i;
return is;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
return os << '(' << p.first << ',' << p.second << ')';
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
for (auto it = v.begin(); it != v.end(); ++it) {
os << (it == v.begin() ? "" : " ") << *it;
}
return os;
}
template <class Head, class... Tail>
void co(Head &&head, Tail &&...tail) {
if constexpr (sizeof...(tail) == 0) std::cout << head << '\n';
else std::cout << head << ' ', co(std::forward<Tail>(tail)...);
}
template <class Head, class... Tail>
void ce(Head &&head, Tail &&...tail) {
if constexpr (sizeof...(tail) == 0) std::cerr << head << '\n';
else std::cerr << head << ' ', ce(std::forward<Tail>(tail)...);
}
template <typename T, typename... Args>
auto make_vector(T x, int arg, Args... args) {
if constexpr (sizeof...(args) == 0) return std::vector<T>(arg, x);
else return std::vector(arg, make_vector<T>(x, args...));
}
void Yes(bool is_correct = true) {
std::cout << (is_correct ? "Yes" : "No") << '\n';
}
void No(bool is_not_correct = true) {
Yes(!is_not_correct);
}
void YES(bool is_correct = true) {
std::cout << (is_correct ? "YES" : "NO") << '\n';
}
void NO(bool is_not_correct = true) {
YES(!is_not_correct);
}
void Takahashi(bool is_correct = true) {
std::cout << (is_correct ? "Takahashi" : "Aoki") << '\n';
}
void Aoki(bool is_not_correct = true) {
Takahashi(!is_not_correct);
}
#line 4 "a.cpp"
using Mint = modint998;
template <class mint>
std::vector<mint> inv(const std::vector<mint> &v) {
return inv(v, v.size());
}
template <class mint>
std::vector<mint> inv(const std::vector<mint> &v, int deg) {
assert(!v.empty() && v[0] != mint(0));
std::vector<mint> res(deg);
res[0] = v[0].inv();
for (int d = 1; d < deg; d <<= 1) {
std::vector<mint> f(2 * d), g(2 * d);
for (int j = 0; j < std::min((int)v.size(), 2 * d); j++) f[j] = v[j];
for (int j = 0; j < d; j++) g[j] = res[j];
internal::butterfly(f);
internal::butterfly(g);
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
internal::butterfly_inv(f);
mint id = mint(2 * d).inv();
for (int i = 0; i < 2 * d; i++) f[i] *= id;
for (int j = 0; j < d; j++) f[j] = 0;
internal::butterfly(f);
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
internal::butterfly_inv(f);
for (int i = 0; i < 2 * d; i++) f[i] *= id;
for (int j = d; j < std::min(2 * d, deg); j++) res[j] = -f[j];
}
res.resize(deg);
return res;
}
pair<vector<Mint>, vector<Mint>> prod(const vector<int> &a, int l, int r, int len) {
if (l + 1 == r) {
return {{1}, {1, -a[l]}};
}
int m = (l + r) / 2;
auto [lp, lq] = prod(a, l, m, len);
auto [rp, rq] = prod(a, m, r, len);
auto q = convolution(lq, rq);
if (q.size() > len)
q.resize(len);
auto p1 = convolution(lp, rq);
auto p2 = convolution(rp, lq);
if (p1.size() > len)
p1.resize(len);
if (p2.size() > len)
p2.resize(len);
if (p1.size() >= p2.size()) {
for (int i = 0; i < (int)p2.size(); ++i) {
p1[i] += p2[i];
}
return {p1, q};
} else {
for (int i = 0; i < (int)p1.size(); ++i) {
p2[i] += p1[i];
}
return {p2, q};
}
}
int main(void) {
int n, m;
cin >> n >> m;
vector<int> a(n);
cin >> a;
auto [ap, aq] = prod(a, 0, n, m + 1);
auto ans = convolution(ap, inv(aq, m + 1));
ans.resize(m + 1);
ans.erase(ans.begin());
co(ans);
return 0;
}