// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1145
#include "../../poly/sum-of-powers.hpp"
#include "../../template.hpp"
#include <atcoder/modint>
using mint = atcoder::modint998244353;
void solve() {
INT(n, m);
vector<mint> a(n);
rep(i, n) {
INT(ai);
a[i] = ai;
}
auto f = sum_of_powers(a, m);
rep(i, 1, m + 1) cout << f[i].val() << " \n"[i == m];
}
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
solve();
}
#line 1 "test/yukicoder/1145.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1145
#line 2 "other/fastio.hpp"
// ref: https://maspypy.com/library-checker-many-a-b , Nyaanさん
#line 2 "other/type-utils.hpp"
#include <bits/stdc++.h>
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using vi = std::vector<int>;
using vii = std::vector<std::vector<int>>;
using pii = std::pair<int, int>;
using vl = std::vector<ll>;
using vll = std::vector<vl>;
using pll = std::pair<ll, ll>;
template <class T>
concept extended_integral =
std::integral<T> || std::same_as<std::remove_cv_t<T>, i128> ||
std::same_as<std::remove_cv_t<T>, u128>;
template <class T>
concept extended_signed_integral =
std::signed_integral<T> || std::same_as<std::remove_cv_t<T>, i128>;
template <class T>
concept extended_unsigned_integral =
std::unsigned_integral<T> || std::same_as<std::remove_cv_t<T>, u128>;
template <class T>
concept Streamable =
requires(std::ostream &os, T &x) { os << x; } || extended_integral<T>;
template <class mint>
concept is_modint = requires(mint &x) {
{ x.val() } -> std::convertible_to<int>;
};
#line 4 "other/fastio.hpp"
namespace fastio {
constexpr int SZ = 1 << 17;
constexpr int offset = 64;
constexpr int mod = 10000;
char in_buf[SZ];
int in_left{}, in_right{};
char out_buf[SZ];
char out_tmp[offset];
int out_right{};
struct Pre {
char num[4 * mod]{};
constexpr Pre() {
for(int i = 0; i < mod; ++i) {
for(int n = i, j = 3; j >= 0; --j, n /= 10)
num[4 * i + j] = '0' + n % 10;
}
}
constexpr const char *operator[](int i) const { return &num[4 * i]; }
} constexpr pre;
void load() {
memmove(in_buf, in_buf + in_left, in_right - in_left);
in_right += -in_left + std::fread(in_buf + in_right - in_left, 1,
SZ - (in_right - in_left), stdin);
in_left = 0;
if(in_right < SZ)
in_buf[in_right++] = '\n';
}
void read(char &c) {
do {
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(isspace(c));
}
void read(std::string &s) {
s.clear();
char c;
do {
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(isspace(c));
do {
s += c;
if(in_left == in_right)
load();
c = in_buf[in_left++];
} while(!isspace(c));
}
template <extended_integral T> void read(T &x) {
if(in_right - in_left < offset)
load();
char c;
do
c = in_buf[in_left++];
while(c < '-'); // \n:10 space:32 -:45 '0':48
bool minus{};
if constexpr(extended_signed_integral<T>) {
if(c == '-') {
c = in_buf[in_left++];
minus = true;
}
}
x = 0;
while(c >= '0') {
x = 10 * x + (c & 15);
c = in_buf[in_left++];
}
if constexpr(extended_signed_integral<T>) {
if(minus)
x = -x;
}
}
void flush() { fwrite(out_buf, 1, std::exchange(out_right, 0), stdout); }
void write_range(const char *c, int n) {
int pos{};
while(pos < n) {
if(out_right == SZ)
flush();
int len = std::min(n - pos, SZ - out_right);
memcpy(out_buf + out_right, c + pos, len);
out_right += len;
pos += len;
}
}
void write(char c) {
if(SZ == out_right)
flush();
out_buf[out_right++] = c;
}
void write(const char *c) { write_range(c, strlen(c)); }
void write(const std::string &s) { write_range(s.data(), s.size()); }
template <std::floating_point T> void write(T x) {
int n = std::snprintf(out_tmp, sizeof(out_tmp), "%.16g", x);
write_range(out_tmp, n);
}
void write(bool x) { write(x ? '1' : '0'); }
template <extended_integral T> void write(T x) {
if(x == 0) {
write('0');
}
if constexpr(extended_signed_integral<T>) {
if(x < 0) {
write('-');
x = -x;
}
}
if(SZ - out_right < offset)
flush();
int cur = offset;
for(; x >= 1000; x /= mod) {
cur -= 4;
memcpy(out_tmp + cur, pre[x % mod], 4);
}
if(x >= 100) {
cur -= 3;
memcpy(out_tmp + cur, pre[x % mod] + 1, 3);
} else if(x >= 10) {
cur -= 2;
memcpy(out_tmp + cur, pre[x % mod] + 2, 2);
} else if(x >= 1) {
cur -= 1;
memcpy(out_tmp + cur, pre[x % mod] + 3, 1);
}
write_range(out_tmp + cur, offset - cur);
}
struct Dummy {
// プログラム終了時に出力
~Dummy() { flush(); }
} dummy;
} // namespace fastio
using fastio::write;
#line 4 "template.hpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#line 8 "template.hpp"
using namespace std;
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...)
#endif
template <Streamable T> void print_one(const T &value) { fastio::write(value); }
template <is_modint T> void print_one(const T &value) {
print_one(value.val());
}
void print() { print_one('\n'); }
template <class T, class... Ts> void print(const T &a, const Ts &...b) {
print_one(a);
((print_one(' '), print_one(b)), ...);
print();
}
template <ranges::range Iterable>
requires(!Streamable<Iterable>)
void print(const Iterable &v) {
for(auto it = v.begin(); it != v.end(); ++it) {
if(it != v.begin())
print_one(' ');
print_one(*it);
}
print();
}
#define all(v) begin(v), end(v)
template <class T> void UNIQUE(T &v) {
ranges::sort(v);
v.erase(unique(all(v)), end(v));
}
template <typename T> inline bool chmax(T &a, T b) {
return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
return ((a > b) ? (a = b, true) : (false));
}
// https://trap.jp/post/1224/
template <class... T> constexpr auto min(T... a) {
return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> constexpr auto max(T... a) {
return max(initializer_list<common_type_t<T...>>{a...});
}
void input() {}
template <class Head, class... Tail> void input(Head &head, Tail &...tail) {
#ifdef LOCAL
cin >> head;
#else
fastio::read(head);
#endif
input(tail...);
}
template <class T> void input(vector<T> &a) {
for(T &x : a)
input(x);
}
#define INT(...) \
int __VA_ARGS__; \
input(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
input(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
input(__VA_ARGS__)
#define REP1_0(n, c) REP1_1(n, c)
#define REP1_1(n, c) \
for(ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(n); REP_COUNTER_##c++)
#define REP1(n) REP1_0(n, __COUNTER__)
#define REP2(i, a) for(ll i = 0; i < (ll)(a); i++)
#define REP3(i, a, b) for(ll i = (ll)(a); i < (ll)(b); i++)
#define REP4(i, a, b, c) for(ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
ll inf = 3e18;
vl dx = {1, -1, 0, 0};
vl dy = {0, 0, 1, -1};
template <class T> constexpr T floor(T x, T y) noexcept {
return x / y - ((x ^ y) < 0 and x % y);
}
template <class T> constexpr T ceil(T x, T y) noexcept {
return x / y + ((x ^ y) >= 0 and x % y);
}
// yの符号に関わらず非負で定義 \bmod:texコマンド
template <class T> constexpr T bmod(T x, T y) noexcept {
T m = x % y;
return (m < 0) ? m + (y > 0 ? y : -y) : m;
}
template <std::signed_integral T> constexpr int bit_width(T x) noexcept {
return std::bit_width((uint64_t)x);
}
template <std::signed_integral T> constexpr int popcount(T x) noexcept {
return std::popcount((uint64_t)x);
}
constexpr bool kth_bit(auto n, auto k) { return (n >> k) & 1; }
#line 3 "poly/formal-power-series.hpp"
#include <atcoder/convolution>
// 10^9+7みたいなときconvolutionどうする？
template <class mint> struct FormalPowerSeries : vector<mint> {
using vector<mint>::vector;
using FPS = FormalPowerSeries;
FormalPowerSeries(const vector<mint> &v) : vector<mint>(v) {}
FPS &operator+=(const FPS &f) {
if(this->size() < f.size())
this->resize(f.size());
for(int i = 0; i < ssize(f); ++i)
(*this)[i] += f[i];
return *this;
}
FPS &operator-=(const FPS &f) {
if(this->size() < f.size())
this->resize(f.size());
for(int i = 0; i < ssize(f); ++i)
(*this)[i] -= f[i];
return *this;
}
FPS &operator*=(const FPS &f) {
if constexpr(is_same_v<mint, long long>) {
return (*this) = atcoder::convolution_ll(*this, f);
} else {
return (*this) = atcoder::convolution(*this, f);
}
}
FPS &operator*=(const mint &x) {
for(mint &vi : *this)
vi *= x;
return *this;
}
FPS operator+(const FPS &f) const { return FPS(*this) += f; }
FPS operator-(const FPS &f) const { return FPS(*this) -= f; }
FPS operator*(const FPS &f) const { return FPS(*this) *= f; }
FPS operator*(const mint &x) const { return FPS(*this) *= x; }
FPS operator-() const {
FPS res = *this;
for(mint &vi : res) {
vi = -vi;
}
return res;
}
FPS operator>>(const int sz) const {
if(sz >= ssize(*this))
return {};
FPS res(begin(*this) + sz, end(*this));
return res;
}
FPS operator<<(const int sz) const {
FPS res(sz, 0);
res.insert(end(res), begin(*this), end(*this));
return res;
}
FPS inv(int deg = -1) const {
assert(!this->empty() and (*this)[0] != mint(0));
if(deg == -1)
deg = this->size();
FPS res = {(*this)[0].inv()};
FPS f;
f.reserve(this->size());
for(int d = 1; d < deg << 1; d <<= 1) {
while(ssize(f) < min(ssize(*this), d))
f.emplace_back((*this)[f.size()]);
res *= (FPS({2}) - f * res);
while(ssize(res) > min(d, deg))
res.pop_back();
}
return res;
}
// なければ空を返す
// 定数項が1でないときget_sqrtを渡す。解が複数ありうることに注意
FPS sqrt(
int deg = -1,
function<mint(mint)> get_sqrt = [](mint) { return mint(1); }) const {
if(this->empty())
return {};
if(deg == -1)
deg = this->size();
if((*this)[0] == mint(0)) {
for(int i = 1; i < ssize(*this); ++i) {
if((*this)[i] == mint(0))
continue;
if(i & 1)
return {};
if(i / 2 >= deg)
break;
FPS res = (*this >> i).sqrt(deg - i / 2, get_sqrt);
if(res.empty())
return {};
res = res << (i / 2);
return res;
}
return FPS(deg, 0);
}
FPS res{get_sqrt((*this)[0])};
if(res[0] * res[0] != (*this)[0])
return {};
FPS f;
f.reserve(this->size());
mint inv2 = mint(1) / mint(2);
for(int d = 1; d < deg << 1; d <<= 1) {
while(ssize(f) < min(ssize(*this), d))
f.emplace_back((*this)[f.size()]);
res = (res + f * res.inv(d)) * inv2;
while(ssize(res) > min(d, deg))
res.pop_back();
}
return res;
}
FPS diff() const {
FPS res(max<int>(0, ssize(*this) - 1));
for(int i = 1; i < ssize(*this); ++i)
res[i - 1] = (mint)i * (*this)[i];
return res;
}
FPS integral() const {
FPS res(ssize(*this) + 1);
for(int i = 0; i < ssize(*this); ++i)
res[i + 1] = (*this)[i] / mint(i + 1);
return res;
}
FPS log(int deg = -1) const {
assert(!this->empty() and (*this)[0] == (mint)1);
if(deg == -1)
deg = this->size();
if(deg == 0)
return {};
FPS t(begin(*this), begin(*this) + min<int>(deg, ssize(*this)));
FPS res = t.diff() * t.inv(deg - 1);
res.resize(deg - 1);
return res.integral();
}
FPS exp(int deg = -1) {
assert(!this->empty() and (*this)[0] == (mint)0);
if(deg == -1)
deg = this->size();
if(deg == 0)
return {};
FPS res = {1};
FPS f;
f.reserve(this->size());
for(int d = 1; d < deg << 1; d <<= 1) {
while(ssize(f) < min(ssize(*this), d))
f.emplace_back((*this)[f.size()]);
res *= (FPS({1}) + f - res.log(d));
while(ssize(res) > min(d, deg))
res.pop_back();
}
return res;
}
};
#line 3 "poly/sum-of-powers.hpp"
/**
* @brief 冪乗和の列挙
* @see https://yukicoder.me/problems/no/1145/editorial
* @see https://maspypy.com/多項式・形式的べき級数-高速に計算できるもの#toc19
* @see https://maspypy.com/多項式・形式的べき級数-高速に計算できるもの#toc34
*/
/// 各i(0≦i≦k)についてsum[j]a_j^iを求め、長さk+1の列を返す
/// O(n*log(n)^2 + k*log(k))時間
template <class mint> vector<mint> sum_of_powers(const vector<mint> &a, int k) {
if(a.empty())
return vector<mint>(k + 1, 0);
queue<FormalPowerSeries<mint>> que;
for(auto &ai : a)
que.push({1, -ai});
while(que.size() > 1) {
auto f = que.front();
que.pop();
auto g = que.front();
que.pop();
que.push(f * g);
}
auto &f = que.front();
f = f.log(k + 1);
for(int i = 1; i <= k; ++i)
f[i] = -f[i] * mint(i);
f[0] = ssize(a);
return f;
}
/// 各i(0≦i≦k)についてsum[j in (0,n]]j^iを求め、長さk+1の列を返す
/// O(k*log(k))時間
template <class mint> vector<mint> sum_of_powers_iota(int n, int k) {
using FPS = FormalPowerSeries<mint>;
FPS num(k + 1, 1), den(k + 1, 1);
mint fac = 1, npow = n;
for(int i = 0; i <= k; ++i, npow *= n) {
num[i] *= npow;
fac *= i + 1;
}
fac = mint(1) / fac;
for(int i = k; i >= 0; --i) {
num[i] *= fac;
den[i] *= fac;
fac *= i + 1;
}
FPS res = num * den.inv(k + 1);
res.resize(k + 1);
fac = 1;
for(int i = 0; i <= k; ++i) {
res[i] *= fac;
fac *= i + 1;
}
return res;
}
#line 4 "test/yukicoder/1145.test.cpp"
#include <atcoder/modint>
using mint = atcoder::modint998244353;
void solve() {
INT(n, m);
vector<mint> a(n);
rep(i, n) {
INT(ai);
a[i] = ai;
}
auto f = sum_of_powers(a, m);
rep(i, 1, m + 1) cout << f[i].val() << " \n"[i == m];
}
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
solve();
}
test/yukicoder/1145.test.cpp