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OI-codes/Luogu/P4512/P4512.cpp

205 lines
4.3 KiB
C++

#include <iostream>
#include <algorithm>
#include <vector>
using std::cin;
using std::cout;
const char endl = '\n';
const int mod = 998244353;
constexpr long long binpow(long long a, long long b) {
a %= mod;
long long res = 1;
while (b) {
if (b & 1) res = res * a % mod;
a = a * a % mod;
b >>= 1;
}
return res;
}
class Poly : public std::vector<long long> {
private:
static void number_theoretic_transform(std::vector<long long> &a) {
if (a.size() == 1) return;
// assert(a.size() == (1 << std::__lg(a.size())));
int k = std::__lg(a.size());
for (int i = 0; i < a.size(); i++) {
int t = 0;
for (int j = 0; j < k; j++) {
if (i & (1 << j)) {
t |= 1 << (k - j - 1);
}
}
if (i < t) std::swap(a[i], a[t]);
}
for (int len = 2; len <= a.size(); len <<= 1) {
int m = len >> 1;
long long wn = binpow(3, (mod - 1) / len);
for (int i = 0; i < a.size(); i += len) {
long long w = 1;
for (int j = 0; j < m; j++) {
long long u = a[i + j],
v = a[i + j + m] * w % mod;
a[i + j] = ((u + v) % mod + mod) % mod;
a[i + j + m] = ((u - v) % mod + mod) % mod;
w = w * wn % mod;
}
}
}
}
static void dft(std::vector<long long> &a) {
number_theoretic_transform(a);
}
static void idft(std::vector<long long> &a) {
number_theoretic_transform(a);
std::reverse(a.begin() + 1, a.end());
long long inv = binpow(a.size(), mod - 2);
std::transform(a.begin(), a.end(), a.begin(), [&](long long x) {
return x * inv % mod;
});
}
public:
using std::vector<long long>::vector;
Poly() = default;
Poly(const std::vector<long long> &__v)
: std::vector<long long>(__v) {}
Poly(std::vector<long long> &&__v)
: std::vector<long long>(std::move(__v)) {}
Poly operator*(const Poly &b) {
int n = size() - 1,
m = b.size() - 1,
k = 1 << (std::__lg(n + m) + 1),
inv = binpow(k, mod - 2);
std::vector<long long> f(*this), g(b);
f.resize(k);
dft(f);
g.resize(k);
dft(g);
for (int i = 0; i < k; i++) {
f[i] = f[i] * g[i] % mod;
}
idft(f);
f.resize(n + m + 1);
return Poly(f);
}
Poly operator/(const Poly &b) {
Poly c{inv(b)};
return *this * c;
}
static Poly inv(Poly a) {
if (a.size() == 1) return Poly{binpow(a[0], mod - 2)};
int n = a.size(),
k = 1 << (std::__lg(n << 1) + 1);
Poly b{a};
a.resize(k);
dft(a);
b.resize(n + 1 >> 1);
b = inv(b);
b.resize(k);
dft(b);
for (int i = 0; i < k; i++) {
b[i] = (2 - a[i] * b[i] % mod + mod) % mod * b[i] % mod;
}
idft(b);
b.resize(n);
return b;
}
static std::pair<Poly, Poly> div(Poly f, Poly g) {
int n = f.size() - 1,
m = g.size() - 1;
Poly rev_f{f}, rev_g{g};
std::reverse(rev_f.begin(), rev_f.end());
std::reverse(rev_g.begin(), rev_g.end());
rev_g.resize(n - m + 1);
rev_g = Poly::inv(rev_g);
rev_f = rev_g * rev_f;
Poly q(n - m + 1), r(m);
for (int i = 0; i <= n - m; i++) {
q[i] = rev_f[n - m - i];
}
g = g * q;
for (int i = 0; i < m; i++) {
r[i] = ((f[i] - g[i]) % mod + mod) % mod;
}
return {q, r};
}
} poly;
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m;
cin >> n >> m;
Poly f(n + 1), g(m + 1);
for (int i = 0; i <= n; i++) {
cin >> f[i];
}
for (int i = 0; i <= m; i++) {
cin >> g[i];
}
auto res = Poly::div(f, g);
Poly q = res.first,
r = res.second;
for (int i = 0; i <= n - m; i++) {
cout << q[i] << ' ';
}
cout << endl;
for (int i = 0; i < m; i++) {
cout << r[i] << ' ';
}
cout << endl;
return 0;
}