結果
| 問題 | No.1307 Rotate and Accumulate |
| ユーザー |
 Haar
|
| 提出日時 | 2020-12-04 12:05:15 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 99 ms / 5,000 ms |
| コード長 | 16,380 bytes |
| コンパイル時間 | 2,445 ms |
| コンパイル使用メモリ | 213,376 KB |
| 最終ジャッジ日時 | 2025-01-16 15:41:52 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 19 |
ソースコード
#line 1 "main.cpp"
#include <bits/stdc++.h>
#ifdef DEBUG
#include <Mylib/Debug/debug.cpp>
#else
#define dump(...) ((void)0)
#endif
template <typename T, typename U>
bool chmin(T &a, const U &b){
return (a > b ? a = b, true : false);
}
template <typename T, typename U>
bool chmax(T &a, const U &b){
return (a < b ? a = b, true : false);
}
template <typename T, size_t N, typename U>
void fill_array(T (&a)[N], const U &v){
std::fill((U*)a, (U*)(a + N), v);
}
template <typename T, size_t N, size_t I = N>
auto make_vector(const std::array<int, N> &a, T value = T()){
static_assert(I >= 1);
static_assert(N >= 1);
if constexpr (I == 1){
return std::vector<T>(a[N - I], value);
}else{
return std::vector(a[N - I], make_vector<T, N, I - 1>(a, value));
}
}
template <typename T>
std::ostream& operator<<(std::ostream &s, const std::vector<T> &a){
for(auto it = a.begin(); it != a.end(); ++it){
if(it != a.begin()) s << " ";
s << *it;
}
return s;
}
template <typename T>
std::istream& operator>>(std::istream &s, std::vector<T> &a){
for(auto &x : a) s >> x;
return s;
}
std::string YesNo(bool value){return value ? "Yes" : "No";}
std::string YESNO(bool value){return value ? "YES" : "NO";}
std::string yesno(bool value){return value ? "yes" : "no";}
template <typename T>
void putl(const T &value){
std::cout << value << "\n";
}
template <typename Head, typename ... Tail>
void putl(const Head head, const Tail &... tail){
std::cout << head << " ";
putl(tail ...);
}
#line 4 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Mint/mint.cpp"
namespace haar_lib {
template <int32_t M>
class modint {
uint32_t val_;
public:
constexpr static auto mod(){return M;}
constexpr modint(): val_(0){}
constexpr modint(int64_t n){
if(n >= M) val_ = n % M;
else if(n < 0) val_ = n % M + M;
else val_ = n;
}
constexpr auto& operator=(const modint &a){val_ = a.val_; return *this;}
constexpr auto& operator+=(const modint &a){
if(val_ + a.val_ >= M) val_ = (uint64_t)val_ + a.val_ - M;
else val_ += a.val_;
return *this;
}
constexpr auto& operator-=(const modint &a){
if(val_ < a.val_) val_ += M;
val_ -= a.val_;
return *this;
}
constexpr auto& operator*=(const modint &a){
val_ = (uint64_t)val_ * a.val_ % M;
return *this;
}
constexpr auto& operator/=(const modint &a){
val_ = (uint64_t)val_ * a.inv().val_ % M;
return *this;
}
constexpr auto operator+(const modint &a) const {return modint(*this) += a;}
constexpr auto operator-(const modint &a) const {return modint(*this) -= a;}
constexpr auto operator*(const modint &a) const {return modint(*this) *= a;}
constexpr auto operator/(const modint &a) const {return modint(*this) /= a;}
constexpr bool operator==(const modint &a) const {return val_ == a.val_;}
constexpr bool operator!=(const modint &a) const {return val_ != a.val_;}
constexpr auto& operator++(){*this += 1; return *this;}
constexpr auto& operator--(){*this -= 1; return *this;}
constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}
constexpr static modint pow(int64_t n, int64_t p){
if(p < 0) return pow(n, -p).inv();
int64_t ret = 1, e = n % M;
for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M;
return ret;
}
constexpr static modint inv(int64_t a){
int64_t b = M, u = 1, v = 0;
while(b){
int64_t t = a / b;
a -= t * b; std::swap(a, b);
u -= t * v; std::swap(u, v);
}
u %= M;
if(u < 0) u += M;
return u;
}
constexpr static auto frac(int64_t a, int64_t b){return modint(a) / modint(b);}
constexpr auto pow(int64_t p) const {return pow(val_, p);}
constexpr auto inv() const {return inv(val_);}
friend constexpr auto operator-(const modint &a){return modint(M - a.val_);}
friend constexpr auto operator+(int64_t a, const modint &b){return modint(a) + b;}
friend constexpr auto operator-(int64_t a, const modint &b){return modint(a) - b;}
friend constexpr auto operator*(int64_t a, const modint &b){return modint(a) * b;}
friend constexpr auto operator/(int64_t a, const modint &b){return modint(a) / b;}
friend std::istream& operator>>(std::istream &s, modint &a){s >> a.val_; return s;}
friend std::ostream& operator<<(std::ostream &s, const modint &a){s << a.val_; return s;}
template <int N>
static auto div(){
static auto value = inv(N);
return value;
}
explicit operator int32_t() const noexcept {return val_;}
explicit operator int64_t() const noexcept {return val_;}
};
}
#line 7 "/home/haar/Downloads/kyopro-lib/Mylib/Convolution/ntt_convolution.cpp"
namespace haar_lib {
template <typename T, int PRIM_ROOT, int MAX_SIZE>
class number_theoretic_transform {
public:
using value_type = T;
constexpr static int primitive_root = PRIM_ROOT;
constexpr static int max_size = MAX_SIZE;
private:
const int MAX_POWER_;
std::vector<T> BASE_, INV_BASE_;
public:
number_theoretic_transform():
MAX_POWER_(__builtin_ctz(MAX_SIZE)),
BASE_(MAX_POWER_ + 1),
INV_BASE_(MAX_POWER_ + 1)
{
static_assert((MAX_SIZE & (MAX_SIZE - 1)) == 0, "MAX_SIZE must be power of 2.");
T t = T::pow(PRIM_ROOT, (T::mod() - 1) >> (MAX_POWER_ + 2));
T s = t.inv();
for(int i = MAX_POWER_; --i >= 0;){
t *= t;
s *= s;
BASE_[i] = -t;
INV_BASE_[i] = -s;
}
}
void run(std::vector<T> &f, bool INVERSE = false) const {
const int n = f.size();
assert((n & (n - 1)) == 0 and n <= MAX_SIZE); // データ数は2の冪乗個
if(INVERSE){
for(int b = 1; b < n; b <<= 1){
T w = 1;
for(int j = 0, k = 1; j < n; j += 2 * b, ++k){
for(int i = 0; i < b; ++i){
const auto s = f[i + j];
const auto t = f[i + j + b];
f[i + j] = s + t;
f[i + j + b] = (s - t) * w;
}
w *= INV_BASE_[__builtin_ctz(k)];
}
}
const T t = T::inv(n);
for(auto &x : f) x *= t;
}else{
for(int b = n >> 1; b; b >>= 1){
T w = 1;
for(int j = 0, k = 1; j < n; j += 2 * b, ++k){
for(int i = 0; i < b; ++i){
const auto s = f[i + j];
const auto t = f[i + j + b] * w;
f[i + j] = s + t;
f[i + j + b] = s - t;
}
w *= BASE_[__builtin_ctz(k)];
}
}
}
}
template <typename U>
std::vector<T> convolve(std::vector<U> f, std::vector<U> g) const {
const int m = f.size() + g.size() - 1;
int n = 1;
while(n < m) n *= 2;
std::vector<T> f2(n), g2(n);
for(int i = 0; i < (int)f.size(); ++i) f2[i] = (int64_t)f[i];
for(int i = 0; i < (int)g.size(); ++i) g2[i] = (int64_t)g[i];
run(f2);
run(g2);
for(int i = 0; i < n; ++i) f2[i] *= g2[i];
run(f2, true);
return f2;
}
template <typename U>
std::vector<T> operator()(std::vector<U> f, std::vector<U> g) const {
return convolve(f, g);
}
};
template <typename T>
std::vector<T> convolve_general_mod(std::vector<T> f, std::vector<T> g){
static constexpr int M1 = 167772161, P1 = 3;
static constexpr int M2 = 469762049, P2 = 3;
static constexpr int M3 = 1224736769, P3 = 3;
auto res1 = number_theoretic_transform<modint<M1>, P1, 1 << 20>().convolve(f, g);
auto res2 = number_theoretic_transform<modint<M2>, P2, 1 << 20>().convolve(f, g);
auto res3 = number_theoretic_transform<modint<M3>, P3, 1 << 20>().convolve(f, g);
const int n = res1.size();
std::vector<T> ret(n);
const int64_t M12 = (int64_t)modint<M2>::inv(M1);
const int64_t M13 = (int64_t)modint<M3>::inv(M1);
const int64_t M23 = (int64_t)modint<M3>::inv(M2);
for(int i = 0; i < n; ++i){
const int64_t r[3] = {(int64_t)res1[i], (int64_t)res2[i], (int64_t)res3[i]};
const int64_t t0 = r[0] % M1;
const int64_t t1 = (r[1] - t0 + M2) * M12 % M2;
const int64_t t2 = ((r[2] - t0 + M3) * M13 % M3 - t1 + M3) * M23 % M3;
ret[i] = T(t0) + T(t1) * M1 + T(t2) * M1 * M2;
}
return ret;
}
}
#line 4 "/home/haar/Downloads/kyopro-lib/Mylib/Math/formal_power_series.cpp"
#include <initializer_list>
#line 6 "/home/haar/Downloads/kyopro-lib/Mylib/Math/formal_power_series.cpp"
namespace haar_lib {
template <typename T, const auto &convolve>
class formal_power_series {
public:
using value_type = T;
private:
std::vector<T> data_;
public:
formal_power_series(){}
explicit formal_power_series(int N): data_(N){}
formal_power_series(const std::vector<T> &data_): data_(data_){}
formal_power_series(std::initializer_list<T> init): data_(init.begin(), init.end()){}
formal_power_series(const formal_power_series &a): data_(a.data_){}
formal_power_series(formal_power_series &&a) noexcept {*this = std::move(a);}
size_t size() const {
return data_.size();
}
const T& operator[](int i) const {
return data_[i];
}
T& operator[](int i){
return data_[i];
}
auto begin() {return data_.begin();}
auto end() {return data_.end();}
const auto& data() const {return data_;}
void resize(int n){
data_.resize(n);
}
auto& operator=(formal_power_series &&rhs) noexcept {
if(this != &rhs){
data_ = std::move(rhs.data_);
}
return *this;
}
auto& operator+=(const formal_power_series &rhs){
if(data_.size() < rhs.size()) data_.resize(rhs.size());
for(int i = 0; i < rhs.size(); ++i) data_[i] += rhs[i];
return *this;
}
auto& operator+=(T rhs){
data_[0] += rhs;
return *this;
}
auto operator+(T rhs) const {
auto ret = *this;
return ret += rhs;
}
auto operator+(const formal_power_series &rhs) const {
auto ret = *this;
return ret += rhs;
}
auto& operator-=(const formal_power_series &rhs){
if(data_.size() < rhs.size()) data_.resize(rhs.size());
for(int i = 0; i < rhs.size(); ++i) data_[i] -= rhs[i];
return *this;
}
auto& operator-=(T rhs){
data_[0] -= rhs;
return *this;
}
auto operator-(T rhs) const {
auto ret = *this;
return ret -= rhs;
}
auto operator-(const formal_power_series &rhs) const {
auto ret = *this;
return ret -= rhs;
}
auto operator-() const {
auto ret = *this;
for(auto &x : ret) x = -x;
return ret;
}
auto& operator*=(const formal_power_series &rhs){
data_ = convolve(data_, rhs.data_);
return *this;
}
auto operator*(const formal_power_series &rhs) const {
auto ret = convolve(data_, rhs.data_);
return formal_power_series(ret);
}
auto& operator*=(T rhs){
for(auto &x : data_) x *= rhs;
return *this;
}
auto operator*(T rhs) const {
auto ret = *this;
return ret *= rhs;
}
auto differentiate() const {
const int n = data_.size();
std::vector<T> ret(n - 1);
for(int i = 0; i < n - 1; ++i){
ret[i] = data_[i + 1] * (i + 1);
}
return formal_power_series(ret);
}
auto integrate() const {
const int n = data_.size();
std::vector<T> ret(n + 1);
for(int i = 0; i < n; ++i){
ret[i + 1] = data_[i] / (i + 1);
}
return formal_power_series(ret);
}
auto inv() const {
assert(data_[0] != 0);
const int n = data_.size();
int t = 1;
std::vector<T> ret = {data_[0].inv()};
ret.reserve(n * 2);
while(t <= n * 2){
std::vector<T> c(data_.begin(), data_.begin() + std::min(t, n));
c = convolve(c, convolve(ret, ret));
c.resize(t);
ret.resize(t);
for(int i = 0; i < t; ++i){
ret[i] = ret[i] * 2 - c[i];
}
t <<= 1;
}
ret.resize(n);
return formal_power_series(ret);
}
auto log() const {
assert(data_[0] == 1);
const int n = data_.size();
auto ret = (differentiate() * inv()).integrate();
ret.resize(n);
return ret;
}
auto exp() const {
const int n = data_.size();
int t = 1;
formal_power_series b({1});
while(t <= n * 2){
t <<= 1;
auto temp = b.log();
temp.resize(t);
for(int i = 0; i < t; ++i) temp[i] = -temp[i];
temp[0] += 1;
for(int i = 0; i < std::min(t, n); ++i) temp[i] += data_[i];
b = b * temp;
b.resize(t);
}
b.resize(n);
return b;
}
auto shift(int64_t k) const {
const int64_t n = data_.size();
formal_power_series ret(n);
if(k >= 0){
for(int64_t i = k; i < n; ++i){
ret[i] = data_[i - k];
}
}else{
for(int64_t i = 0; i < n + k; ++i){
ret[i] = data_[i - k];
}
}
return ret;
}
auto pow(int64_t M) const {
assert(M >= 0);
const int n = data_.size();
int k = 0;
for(; k < n; ++k){
if(data_[k] != 0){
break;
}
}
if(k >= n) return *this;
T a = data_[k];
formal_power_series ret = *this;
ret = (ret.shift(-k)) * a.inv();
ret = (ret.log() * (T)M).exp();
ret = (ret * a.pow(M)).shift(M * k);
return ret;
}
std::optional<formal_power_series> sqrt() const;
};
}
#line 3 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Mod/mod_pow.cpp"
namespace haar_lib {
constexpr int64_t mod_pow(int64_t n, int64_t p, int64_t m){
int64_t ret = 1;
while(p > 0){
if(p & 1) (ret *= n) %= m;
(n *= n) %= m;
p >>= 1;
}
return ret;
}
}
#line 3 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Prime/primitive_root.cpp"
namespace haar_lib {
constexpr int primitive_root(int p){
int pf[30] = {};
int k = 0;
{
int n = p - 1;
for(int64_t i = 2; i * i <= p; ++i){
if(n % i == 0){
pf[k++] = i;
while(n % i == 0) n /= i;
}
}
if(n != 1)
pf[k++] = n;
}
for(int g = 2; g <= p; ++g){
bool ok = true;
for(int i = 0; i < k; ++i){
if(mod_pow(g, (p - 1) / pf[i], p) == 1){
ok = false;
break;
}
}
if(not ok) continue;
return g;
}
return -1;
}
}
#line 5 "/home/haar/Downloads/kyopro-lib/Mylib/IO/join.cpp"
namespace haar_lib {
template <typename Iter>
std::string join(Iter first, Iter last, std::string delim = " "){
std::stringstream s;
for(auto it = first; it != last; ++it){
if(it != first) s << delim;
s << *it;
}
return s.str();
}
}
#line 70 "main.cpp"
namespace haar_lib {}
namespace solver {
using namespace haar_lib;
constexpr int m1000000007 = 1000000007;
constexpr int m998244353 = 998244353;
void init(){
std::cin.tie(0);
std::ios::sync_with_stdio(false);
std::cout << std::fixed << std::setprecision(12);
std::cerr << std::fixed << std::setprecision(12);
std::cin.exceptions(std::ios_base::failbit);
}
using mint = modint<m998244353>;
constexpr int prim_root = primitive_root(m998244353);
const static auto ntt = number_theoretic_transform<mint, prim_root, 1 << 21>();
using FPS = formal_power_series<mint, ntt>;
void solve(){
int N, Q; std::cin >> N >> Q;
std::vector<int> a(N); std::cin >> a;
std::vector<int> r(Q); std::cin >> r;
std::vector<mint> s(N);
for(int x : r){
s[N - 1 - x] += 1;
}
std::vector<mint> t(a.begin(), a.end());
t.insert(t.end(), a.begin(), a.end());
auto res = FPS(s) * FPS(t);
dump(res.data());
std::cout << join(res.begin() + N - 1, res.begin() + (2 * N - 1)) << "\n";
}
}
int main(){
solver::init();
while(true){
try{
solver::solve();
std::cout << std::flush;
std::cerr << std::flush;
}catch(const std::istream::failure &e){
break;
}catch(...){
break;
}
}
return 0;
}