// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/shift_of_sampling_points_of_polynomial
#include <atcoder/modint>
using mint = atcoder::modint998244353;
#include "../../../poly/shift-of-sampling-points.hpp"
#include "../../../template.hpp"
void solve() {
LL(n, m, c);
vector<mint> f(n);
rep(i, n) {
LL(fi);
f[i] = fi;
}
auto res = shift_of_sampling_points(f, m, c);
print(res);
}
int main() {
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
solve();
}
#line 1 "test/library_checker/polynomial/shift_of_sampling_points_of_polynomial.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/shift_of_sampling_points_of_polynomial
#include <atcoder/modint>
using mint = atcoder::modint998244353;
#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 "math/factorial.hpp"
// 参考 https://suisen-cp.github.io/cp-library-cpp/library/math/factorial.hpp
template <class T> struct factorial {
factorial() {};
void ensure(int n) {
auto &fac = get_fac();
auto &fac_inv = get_fac_inv();
int sz = size(fac);
if(sz > n) {
return;
}
int new_sz = max(2 * sz, n + 1);
fac.resize(new_sz), fac_inv.resize(new_sz);
for(int i = sz; i < new_sz; ++i) {
fac[i] = fac[i - 1] * i;
}
fac_inv[new_sz - 1] = T(1) / fac[new_sz - 1];
for(int i = new_sz - 2; i >= sz; --i) {
fac_inv[i] = fac_inv[i + 1] * (i + 1);
}
}
T operator[](int i) {
ensure(i);
return get_fac()[i];
}
T inv(int i) {
ensure(i);
return get_fac_inv()[i];
}
T binom(int n, int i) {
if(n < 0 or i < 0 or n < i) {
return T(0);
}
ensure(n);
return get_fac()[n] * get_fac_inv()[i] * get_fac_inv()[n - i];
}
T perm(int n, int i) {
if(n < 0 or i < 0 or n < i) {
return T(0);
}
ensure(n);
return get_fac()[n] * get_fac_inv()[n - i];
}
private:
/*
inline static vector<T> fac{1};
のように書くと static initialization order fiasco と呼ばれる問題が起きる
この問題を避けるため、関数内の static 変数として定義するイディオム
(Construct on First Use / Meyers' Singleton) を用いる
https://in-neuro.hatenablog.com/entry/2020/12/12/001244
*/
static auto &get_fac() {
static vector<T> fac_{1};
return fac_;
}
static auto &get_fac_inv() {
static vector<T> fac_inv_{1};
return fac_inv_;
}
};
#line 3 "poly/shift-of-sampling-points.hpp"
#include <atcoder/convolution>
// https://suisen-cp.github.io/cp-library-cpp/library/polynomial/shift_of_sampling_points.hpp
template <class Mint>
vector<Mint> shift_of_sampling_points(const vector<Mint> &f, const int m,
const int c) {
// n次未満の多項式fのn個の点f(0),...,f(n-1)に対して
// f(c),...,f(c+m-1)を計算
factorial<Mint> fac;
const int n = f.size();
auto a = [&] {
vector<Mint> a1(n), a2(n);
rep(i, n) {
a1[i] = f[i] * fac.inv(i);
a2[i] = ((i & 1) ? -1 : 1) * fac.inv(i);
}
auto a = convolution(a1, a2);
a.resize(n);
return a;
}();
vector<Mint> a_(n);
rep(i, n) { a_[i] = a[n - 1 - i] * fac[n - 1 - i]; }
vector<Mint> b2 = [&] {
// b2[i] = c*(c-1)*...*(c-i+1)/i!
vector<Mint> b2(n);
Mint ci = 1;
b2[0] = ci;
for(int i = 1; i < n; i++) {
ci *= c - i + 1;
b2[i] = ci * fac.inv(i);
}
return b2;
}();
auto b = convolution(a_, b2);
vector<Mint> fc = [&] {
vector<Mint> f1(n);
vector<Mint> f2(m);
rep(i, n) { f1[i] = b[n - 1 - i] * fac.inv(i); }
rep(i, m) { f2[i] = fac.inv(i); }
return convolution(f1, f2);
}();
vector<Mint> res(m);
rep(i, m) { res[i] = fac[i] * fc[i]; }
return res;
}
#line 6 "test/library_checker/polynomial/shift_of_sampling_points_of_polynomial.test.cpp"
void solve() {
LL(n, m, c);
vector<mint> f(n);
rep(i, n) {
LL(fi);
f[i] = fi;
}
auto res = shift_of_sampling_points(f, m, c);
print(res);
}
int main() {
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
solve();
}
test/library_checker/polynomial/shift_of_sampling_points_of_polynomial.test.cpp