compro_library
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test/library-checker/convolution/convolution-mod.test.cpp
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- Last update: 2024-09-08 23:17:50+09:00
- Problem: https://judge.yosupo.jp/problem/convolution_mod
Depends on
- math/convolution/ntt.hpp
- math/pow_mod.hpp
- math/primitive-root.hpp
- modint/modint.hpp
- template/template.cpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod"
#include "../../../template/template.cpp"
#include "../../../modint/modint.hpp"
#include "../../../math/convolution/ntt.hpp"
int main() {
INT(N, M);
using mint = ModInt<MOD2>;
vector<mint> a(N), b(M);
REP(i, N) cin >> a[i];
REP(i, M) cin >> b[i];
auto c = ntt::convolution<mint>(a, b);
REP(i, N + M - 1) cout << c[i] << " \n"[i == N + M - 2];
}#line 1 "test/library-checker/convolution/convolution-mod.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod"
#line 1 "template/template.cpp"
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
// input output utils
namespace siro53_io {
// https://maspypy.github.io/library/other/io_old.hpp
struct has_val_impl {
template <class T>
static auto check(T &&x) -> decltype(x.val(), std::true_type{});
template <class T> static auto check(...) -> std::false_type;
};
template <class T>
class has_val : public decltype(has_val_impl::check<T>(std::declval<T>())) {
};
// debug
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void dump(const T t) {
cerr << t;
}
template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
void dump(const T t) {
cerr << t;
}
template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
void dump(const T &t) {
cerr << t.val();
}
void dump(__int128_t n) {
if(n == 0) {
cerr << '0';
return;
} else if(n < 0) {
cerr << '-';
n = -n;
}
string s;
while(n > 0) {
s += (char)('0' + n % 10);
n /= 10;
}
reverse(s.begin(), s.end());
cerr << s;
}
void dump(const string &s) { cerr << s; }
void dump(const char *s) {
int n = (int)strlen(s);
for(int i = 0; i < n; i++) cerr << s[i];
}
template <class T1, class T2> void dump(const pair<T1, T2> &p) {
cerr << '(';
dump(p.first);
cerr << ',';
dump(p.second);
cerr << ')';
}
template <class T> void dump(const vector<T> &v) {
cerr << '{';
for(int i = 0; i < (int)v.size(); i++) {
dump(v[i]);
if(i < (int)v.size() - 1) cerr << ',';
}
cerr << '}';
}
template <class T> void dump(const set<T> &s) {
cerr << '{';
for(auto it = s.begin(); it != s.end(); it++) {
dump(*it);
if(next(it) != s.end()) cerr << ',';
}
cerr << '}';
}
template <class Key, class Value> void dump(const map<Key, Value> &mp) {
cerr << '{';
for(auto it = mp.begin(); it != mp.end(); it++) {
dump(*it);
if(next(it) != mp.end()) cerr << ',';
}
cerr << '}';
}
template <class Key, class Value>
void dump(const unordered_map<Key, Value> &mp) {
cerr << '{';
for(auto it = mp.begin(); it != mp.end(); it++) {
dump(*it);
if(next(it) != mp.end()) cerr << ',';
}
cerr << '}';
}
template <class T> void dump(const deque<T> &v) {
cerr << '{';
for(int i = 0; i < (int)v.size(); i++) {
dump(v[i]);
if(i < (int)v.size() - 1) cerr << ',';
}
cerr << '}';
}
template <class T> void dump(queue<T> q) {
cerr << '{';
while(!q.empty()) {
dump(q.front());
if((int)q.size() > 1) cerr << ',';
q.pop();
}
cerr << '}';
}
void debug_print() { cerr << endl; }
template <class Head, class... Tail>
void debug_print(const Head &h, const Tail &...t) {
dump(h);
if(sizeof...(Tail)) dump(' ');
debug_print(t...);
}
// print
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void print_single(const T t) {
cout << t;
}
template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
void print_single(const T t) {
cout << t;
}
template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
void print_single(const T t) {
cout << t.val();
}
void print_single(__int128_t n) {
if(n == 0) {
cout << '0';
return;
} else if(n < 0) {
cout << '-';
n = -n;
}
string s;
while(n > 0) {
s += (char)('0' + n % 10);
n /= 10;
}
reverse(s.begin(), s.end());
cout << s;
}
void print_single(const string &s) { cout << s; }
void print_single(const char *s) {
int n = (int)strlen(s);
for(int i = 0; i < n; i++) cout << s[i];
}
template <class T1, class T2> void print_single(const pair<T1, T2> &p) {
print_single(p.first);
cout << ' ';
print_single(p.second);
}
template <class T> void print_single(const vector<T> &v) {
for(int i = 0; i < (int)v.size(); i++) {
print_single(v[i]);
if(i < (int)v.size() - 1) cout << ' ';
}
}
template <class T> void print_single(const set<T> &s) {
for(auto it = s.begin(); it != s.end(); it++) {
print_single(*it);
if(next(it) != s.end()) cout << ' ';
}
}
template <class T> void print_single(const deque<T> &v) {
for(int i = 0; i < (int)v.size(); i++) {
print_single(v[i]);
if(i < (int)v.size() - 1) cout << ' ';
}
}
template <class T> void print_single(queue<T> q) {
while(!q.empty()) {
print_single(q.front());
if((int)q.size() > 1) cout << ' ';
q.pop();
}
}
void print() { cout << '\n'; }
template <class Head, class... Tail>
void print(const Head &h, const Tail &...t) {
print_single(h);
if(sizeof...(Tail)) print_single(' ');
print(t...);
}
// input
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void input_single(T &t) {
cin >> t;
}
template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
void input_single(T &t) {
cin >> t;
}
template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
void input_single(T &t) {
cin >> t;
}
void input_single(__int128_t &n) {
string s;
cin >> s;
if(s == "0") {
n = 0;
return;
}
bool is_minus = false;
if(s[0] == '-') {
s = s.substr(1);
is_minus = true;
}
n = 0;
for(int i = 0; i < (int)s.size(); i++) n = n * 10 + (int)(s[i] - '0');
if(is_minus) n = -n;
}
void input_single(string &s) { cin >> s; }
template <class T1, class T2> void input_single(pair<T1, T2> &p) {
input_single(p.first);
input_single(p.second);
}
template <class T> void input_single(vector<T> &v) {
for(auto &e : v) input_single(e);
}
void input() {}
template <class Head, class... Tail> void input(Head &h, Tail &...t) {
input_single(h);
input(t...);
}
}; // namespace siro53_io
#ifdef DEBUG
#define debug(...) \
cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debug_print(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
// io setup
struct Setup {
Setup() {
cin.tie(0);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} __Setup;
using namespace siro53_io;
// types
using ll = long long;
using i128 = __int128_t;
// input macros
#define INT(...) \
int __VA_ARGS__; \
input(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
input(__VA_ARGS__)
#define STRING(...) \
string __VA_ARGS__; \
input(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
input(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
input(__VA_ARGS__)
#define LD(...) \
long double __VA_ARGS__; \
input(__VA_ARGS__)
#define UINT(...) \
unsigned int __VA_ARGS__; \
input(__VA_ARGS__)
#define ULL(...) \
unsigned long long __VA_ARGS__; \
input(__VA_ARGS__)
#define VEC(name, type, len) \
vector<type> name(len); \
input(name);
#define VEC2(name, type, len1, len2) \
vector name(len1, vector<type>(len2)); \
input(name);
// other macros
// https://trap.jp/post/1224/
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
#define REP1(i, n) for(int i = 0; i < int(n); i++)
#define REP2(i, a, b) for(int i = (a); i < int(b); i++)
#define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define SORT(v) sort(ALL(v))
#define RSORT(v) sort(RALL(v))
#define UNIQUE(v) \
sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()), v.shrink_to_fit()
#define REV(v) reverse(ALL(v))
#define SZ(v) ((int)(v).size())
#define MIN(v) (*min_element(ALL(v)))
#define MAX(v) (*max_element(ALL(v)))
// util const
const int INF = 1 << 30;
const ll LLINF = 1LL << 60;
constexpr int MOD = 1000000007;
constexpr int MOD2 = 998244353;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
// util functions
void Case(int i) { cout << "Case #" << i << ": "; }
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
template <class T> inline bool chmax(T &a, T b) {
return (a < b ? a = b, true : false);
}
template <class T> inline bool chmin(T &a, T b) {
return (a > b ? a = b, true : false);
}
template <class T, int dim>
auto make_vector_impl(vector<int>& sizes, const T &e) {
if constexpr(dim == 1) {
return vector(sizes[0], e);
} else {
int n = sizes[dim - 1];
sizes.pop_back();
return vector(n, make_vector_impl<T, dim - 1>(sizes, e));
}
}
template <class T, int dim>
auto make_vector(const int (&sizes)[dim], const T &e = T()) {
vector<int> s(dim);
for(int i = 0; i < dim; i++) s[i] = sizes[dim - i - 1];
return make_vector_impl<T, dim>(s, e);
}
vector<int> iota_gen(int n, int start = 0) {
vector<int> ord(n);
iota(ord.begin(), ord.end(), start);
return ord;
}
template<typename T>
vector<int> ord_sort(const vector<T>& v, bool greater = false) {
auto ord = iota_gen((int)v.size());
sort(ALL(ord), [&](int i, int j) {
if(greater) return v[i] > v[j];
return v[i] < v[j];
});
return ord;
}
#pragma endregion Macros
#line 2 "modint/modint.hpp"
#line 6 "modint/modint.hpp"
template <int mod> class ModInt {
public:
ModInt() : x(0) {}
ModInt(long long y)
: x(y >= 0 ? y % umod() : (umod() - (-y) % umod()) % umod()) {}
unsigned int val() const { return x; }
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= umod()) x -= umod();
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += umod() - p.x) >= umod()) x -= umod();
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (unsigned int)(1ULL * x * p.x % umod());
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inv();
return *this;
}
ModInt operator-() const { return ModInt(-(long long)x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inv() const {
long long a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
std::swap(a -= t * b, b);
std::swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(unsigned long long n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, ModInt &a) {
long long t;
is >> t;
a = ModInt<mod>(t);
return (is);
}
static constexpr int get_mod() { return mod; }
private:
unsigned int x;
static constexpr unsigned int umod() { return mod; }
};
#line 2 "math/convolution/ntt.hpp"
#line 6 "math/convolution/ntt.hpp"
#line 2 "math/primitive-root.hpp"
#line 2 "math/pow_mod.hpp"
constexpr long long pow_mod(long long x, long long k, long long m) {
long long res = 1;
long long mul = (x >= 0 ? x % m : x % m + m);
while(k) {
if(k & 1) res = (__int128_t)res * mul % m;
mul = (__int128_t)mul * mul % m;
k >>= 1;
}
return res;
}
#line 4 "math/primitive-root.hpp"
constexpr int primitive_root(int p) {
if(p == 2) return 1;
if(p == 998244353) return 3;
int primes[31] = {};
int sz = 0, t = p - 1;
for(int i = 2; i * i <= t; i++) {
if(t % i == 0) {
primes[sz++] = i;
while(t % i == 0) t /= i;
}
}
if(t > 1) primes[sz++] = t;
for(int g = 2;;g++) {
bool f = true;
for(int i = 0; i < sz; i++) {
if(pow_mod(g, (p - 1) / primes[i], p) == 1) {
f = false;
break;
}
}
if(f) return g;
}
}
#line 9 "math/convolution/ntt.hpp"
namespace ntt {
constexpr int exp_limit(int mod) { return __builtin_ctz(mod - 1); }
template <class mint, int mod = mint::get_mod(),
int g = primitive_root(mod)>
struct ntt_info {
static constexpr int limit = exp_limit(mod);
std::array<mint, limit + 1> root;
std::array<mint, limit + 1> iroot;
ntt_info() {
root[limit] = mint(g).pow((mod - 1) >> limit);
iroot[limit] = root[limit].inv();
for(int i = limit - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
}
};
inline uint64_t revbit(uint64_t mask) {
int b = __builtin_clzll(mask);
uint64_t x = mask;
x = (x >> 32) | (x << 32);
x = ((x >> 16) & 0x0000FFFF0000FFFF) | ((x << 16) & 0xFFFF0000FFFF0000);
x = ((x >> 8) & 0x00FF00FF00FF00FF) | ((x << 8) & 0xFF00FF00FF00FF00);
x = ((x >> 4) & 0x0F0F0F0F0F0F0F0F) | ((x << 4) & 0xF0F0F0F0F0F0F0F0);
x = ((x >> 2) & 0x3333333333333333) | ((x << 2) & 0xCCCCCCCCCCCCCCCC);
x = ((x >> 1) & 0x5555555555555555) | ((x << 1) & 0xAAAAAAAAAAAAAAAA);
return (x >> b);
}
template<class mint>
void ntt(std::vector<mint>& a) {
int n = (int)a.size();
int bitlen = __builtin_ctz(n);
static const ntt_info<mint> info;
for(int len = n, b = bitlen; len > 1; len >>= 1, b--) {
for(int i = 0; i < n; i += len) {
int t = len >> 1;
mint wj = 1;
for(int j = 0; j < t; j++) {
int p = i + j;
mint l = a[p] + a[p + t];
mint r = (a[p] - a[p + t]) * wj;
a[p] = l, a[p + t] = r;
wj *= info.root[b];
}
}
}
for(int i = 0; i < n; i++) {
int j = revbit(i);
if(i < j) std::swap(a[i], a[j]);
}
}
template<class mint>
void intt(std::vector<mint>& a) {
int n = (int)a.size();
static const ntt_info<mint> info;
for(int i = 0; i < n; i++) {
int j = revbit(i);
if(i < j) std::swap(a[i], a[j]);
}
for(int len = 2, b = 1; len <= n; len <<= 1, b++) {
for(int i = 0; i < n; i += len) {
int t = len >> 1;
mint wj = 1;
for(int j = 0; j < t; j++) {
int p = i + j;
auto l = a[p] + a[p + t] * wj;
auto r = a[p] - a[p + t] * wj;
a[p] = l, a[p + t] = r;
wj *= info.iroot[b];
}
}
}
mint invn = mint(n).inv();
for(int i = 0; i < n; i++) a[i] *= invn;
}
template<class mint>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int m = (int)a.size() + (int)b.size() - 1;
int n = 1;
while(n < m) n <<= 1;
a.resize(n), b.resize(n);
ntt<mint>(a);
ntt<mint>(b);
for(int i = 0; i < n; i++) a[i] *= b[i];
intt<mint>(a);
a.resize(m);
return a;
}
}; // namespace ntt
#line 5 "test/library-checker/convolution/convolution-mod.test.cpp"
int main() {
INT(N, M);
using mint = ModInt<MOD2>;
vector<mint> a(N), b(M);
REP(i, N) cin >> a[i];
REP(i, M) cin >> b[i];
auto c = ntt::convolution<mint>(a, b);
REP(i, N + M - 1) cout << c[i] << " \n"[i == N + M - 2];
}