結果
| 問題 | No.1080 Strange Squared Score Sum |
| ユーザー |
 yosupot
|
| 提出日時 | 2020-05-02 19:38:06 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,599 ms / 5,000 ms |
| コード長 | 22,409 bytes |
| コンパイル時間 | 2,185 ms |
| コンパイル使用メモリ | 154,644 KB |
| 実行使用メモリ | 62,408 KB |
| 最終ジャッジ日時 | 2024-06-10 14:14:28 |
| 合計ジャッジ時間 | 19,616 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,940 KB |
| testcase_02 | AC | 743 ms
33,088 KB |
| testcase_03 | AC | 1,558 ms
61,296 KB |
| testcase_04 | AC | 347 ms
18,172 KB |
| testcase_05 | AC | 351 ms
18,400 KB |
| testcase_06 | AC | 79 ms
7,008 KB |
| testcase_07 | AC | 159 ms
10,728 KB |
| testcase_08 | AC | 746 ms
32,928 KB |
| testcase_09 | AC | 753 ms
32,440 KB |
| testcase_10 | AC | 79 ms
7,136 KB |
| testcase_11 | AC | 1,557 ms
61,244 KB |
| testcase_12 | AC | 747 ms
32,416 KB |
| testcase_13 | AC | 1,580 ms
61,368 KB |
| testcase_14 | AC | 753 ms
32,784 KB |
| testcase_15 | AC | 2 ms
6,944 KB |
| testcase_16 | AC | 1,599 ms
62,408 KB |
| testcase_17 | AC | 733 ms
34,428 KB |
| testcase_18 | AC | 731 ms
34,432 KB |
| testcase_19 | AC | 744 ms
34,428 KB |
| testcase_20 | AC | 1,594 ms
61,372 KB |
| testcase_21 | AC | 1,575 ms
61,228 KB |
ソースコード
//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx")
//#undef LOCAL
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <complex>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
struct Scanner {
FILE* fp = nullptr;
char line[(1 << 15) + 1];
size_t st = 0, ed = 0;
void reread() {
memmove(line, line + st, ed - st);
ed -= st;
st = 0;
ed += fread(line + ed, 1, (1 << 15) - ed, fp);
line[ed] = '\0';
}
bool succ() {
while (true) {
if (st == ed) {
reread();
if (st == ed) return false;
}
while (st != ed && isspace(line[st])) st++;
if (st != ed) break;
}
if (ed - st <= 50) reread();
return true;
}
template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
bool read_single(T& ref) {
if (!succ()) return false;
while (true) {
size_t sz = 0;
while (st + sz < ed && !isspace(line[st + sz])) sz++;
ref.append(line + st, sz);
st += sz;
if (!sz || st != ed) break;
reread();
}
return true;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
bool read_single(T& ref) {
if (!succ()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
ref = T(0);
while (isdigit(line[st])) {
ref = 10 * ref + (line[st++] - '0');
}
if (neg) ref = -ref;
return true;
}
template <class T> bool read_single(V<T>& ref) {
for (auto& d : ref) {
if (!read_single(d)) return false;
}
return true;
}
void read() {}
template <class H, class... T> void read(H& h, T&... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
Scanner(FILE* _fp) : fp(_fp) {}
};
struct Printer {
public:
template <bool F = false> void write() {}
template <bool F = false, class H, class... T>
void write(const H& h, const T&... t) {
if (F) write_single(' ');
write_single(h);
write<true>(t...);
}
template <class... T> void writeln(const T&... t) {
write(t...);
write_single('\n');
}
Printer(FILE* _fp) : fp(_fp) {}
~Printer() { flush(); }
private:
static constexpr size_t SIZE = 1 << 15;
FILE* fp;
char line[SIZE], small[50];
size_t pos = 0;
void flush() {
fwrite(line, 1, pos, fp);
pos = 0;
}
void write_single(const char& val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void write_single(T val) {
if (pos > (1 << 15) - 50) flush();
if (val == 0) {
write_single('0');
return;
}
if (val < 0) {
write_single('-');
val = -val; // todo min
}
size_t len = 0;
while (val) {
small[len++] = char('0' + (val % 10));
val /= 10;
}
for (size_t i = 0; i < len; i++) {
line[pos + i] = small[len - 1 - i];
}
pos += len;
}
void write_single(const string& s) {
for (char c : s) write_single(c);
}
void write_single(const char* s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write_single(s[i]);
}
template <class T> void write_single(const V<T>& val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write_single(' ');
write_single(val[i]);
}
}
};
template <uint MD> struct ModInt {
using M = ModInt;
static constexpr uint get_mod() { return MD; }
const static M G;
uint v;
ModInt(ll _v = 0) { set_v(uint(_v % MD + MD)); }
M& set_v(uint _v) {
v = (_v < MD) ? _v : _v - MD;
return *this;
}
explicit operator bool() const { return v != 0; }
M operator-() const { return M() - *this; }
M operator+(const M& r) const { return M().set_v(v + r.v); }
M operator-(const M& r) const { return M().set_v(v + MD - r.v); }
M operator*(const M& r) const { return M().set_v(uint(ull(v) * r.v % MD)); }
M operator/(const M& r) const { return *this * r.inv(); }
M& operator+=(const M& r) { return *this = *this + r; }
M& operator-=(const M& r) { return *this = *this - r; }
M& operator*=(const M& r) { return *this = *this * r; }
M& operator/=(const M& r) { return *this = *this / r; }
bool operator==(const M& r) const { return v == r.v; }
M pow(ll n) const {
M x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
M inv() const { return pow(MD - 2); }
friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; }
};
// using Mint = ModInt<998244353>;
// template<> const Mint Mint::G = Mint(3);
template<class Mint>
struct Comb {
int max_n;
V<Mint> fact, ifact;
Comb() {}
Comb(int n) : max_n(n) {
fact = ifact = V<Mint>(n + 1);
fact[0] = Mint(1);
for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * i;
ifact[n] = fact[n].inv();
for (int i = n; i >= 1; i--) ifact[i - 1] = ifact[i] * i;
}
Mint C(int n, int k) {
if (n < k || n < 0) return Mint(0);
assert(0 <= k && k <= n && n <= max_n);
return fact[n] * ifact[k] * ifact[n - k];
}
};
using Mint = ModInt<TEN(9) + 9>;
Mint i_mod = 430477711; // i_mod * i_mod == -1
using D = double;
const D PI = acos(D(-1));
using Pc = complex<D>;
void fft(bool type, V<Pc>& a) {
int n = int(a.size()), s = 0;
while ((1 << s) < n) s++;
assert(1 << s == n);
static V<Pc> ep[30];
if (!ep[s].size()) {
for (int i = 0; i < n; i++) {
ep[s].push_back(polar<D>(1, i * 2 * PI / n));
}
}
V<Pc> b(n);
for (int i = 1; i <= s; i++) {
int w = 1 << (s - i);
for (int y = 0; y < n / 2; y += w) {
Pc now = ep[s][y];
if (type) now = conj(now);
for (int x = 0; x < w; x++) {
auto l = a[y << 1 | x];
auto u = now, v = a[y << 1 | x | w];
auto r = Pc(u.real() * v.real() - u.imag() * v.imag(),
u.real() * v.imag() + u.imag() * v.real());
b[y | x] = l + r;
b[y | x | n >> 1] = l - r;
}
}
swap(a, b);
}
}
V<Pc> multiply(const V<Pc>& a, const V<Pc>& b) {
int A = int(a.size()), B = int(b.size());
if (!A || !B) return {};
int lg = 0;
while ((1 << lg) < A + B - 1) lg++;
int N = 1 << lg;
V<Pc> ac(N), bc(N);
for (int i = 0; i < A; i++) ac[i] = a[i];
for (int i = 0; i < B; i++) bc[i] = b[i];
fft(false, ac);
fft(false, bc);
for (int i = 0; i < N; i++) {
ac[i] *= bc[i];
}
fft(true, ac);
V<Pc> c(A + B - 1);
for (int i = 0; i < A + B - 1; i++) {
c[i] = ac[i] / D(N);
}
return c;
}
V<D> multiply(const V<D>& a, const V<D>& b) {
int A = int(a.size()), B = int(b.size());
if (!A || !B) return {};
int lg = 0;
while ((1 << lg) < A + B - 1) lg++;
int N = 1 << lg;
V<Pc> d(N);
for (int i = 0; i < N; i++) d[i] = Pc(i < A ? a[i] : 0, i < B ? b[i] : 0);
fft(false, d);
for (int i = 0; i < N / 2 + 1; i++) {
auto j = i ? (N - i) : 0;
Pc x = Pc(d[i].real() + d[j].real(), d[i].imag() - d[j].imag());
Pc y = Pc(d[i].imag() + d[j].imag(), -d[i].real() + d[j].real());
d[i] = x * y / D(4);
if (i != j) d[j] = conj(d[i]);
}
fft(true, d);
V<D> c(A + B - 1);
for (int i = 0; i < A + B - 1; i++) {
c[i] = d[i].real() / N;
}
return c;
}
template <class Mint, int K = 3, int SHIFT = 11>
V<Mint> multiply(const V<Mint>& a, const V<Mint>& b) {
int A = int(a.size()), B = int(b.size());
if (!A || !B) return {};
int lg = 0;
while ((1 << lg) < A + B - 1) lg++;
int N = 1 << lg;
VV<Pc> x(K, V<Pc>(N)), y(K, V<Pc>(N));
for (int ph = 0; ph < K; ph++) {
V<Pc> z(N);
for (int i = 0; i < N; i++) {
D nx = 0, ny = 0;
if (i < A) nx = (a[i].v >> (ph * SHIFT)) & ((1 << SHIFT) - 1);
if (i < B) ny = (b[i].v >> (ph * SHIFT)) & ((1 << SHIFT) - 1);
z[i] = Pc(nx, ny);
}
fft(false, z);
for (int i = 0; i < N; i++) {
z[i] *= 0.5;
}
for (int i = 0; i < N; i++) {
int j = (i) ? N - i : 0;
x[ph][i] = Pc(z[i].real() + z[j].real(), z[i].imag() - z[j].imag());
y[ph][i] =
Pc(z[i].imag() + z[j].imag(), -z[i].real() + z[j].real());
}
}
VV<Pc> z(K, V<Pc>(N));
for (int xp = 0; xp < K; xp++) {
for (int yp = 0; yp < K; yp++) {
int zp = (xp + yp) % K;
for (int i = 0; i < N; i++) {
if (xp + yp < K) {
z[zp][i] += x[xp][i] * y[yp][i];
} else {
z[zp][i] += x[xp][i] * y[yp][i] * Pc(0, 1);
}
}
}
}
for (int ph = 0; ph < K; ph++) {
fft(true, z[ph]);
}
V<Mint> c(A + B - 1);
Mint base = 1;
for (int ph = 0; ph < 2 * K - 1; ph++) {
for (int i = 0; i < A + B - 1; i++) {
if (ph < K) {
c[i] += Mint(ll(round(z[ph][i].real() / N))) * base;
} else {
c[i] += Mint(ll(round(z[ph - K][i].imag() / N))) * base;
}
}
base *= 1 << SHIFT;
}
return c;
}
#include <cstdint>
#include <random>
#include <chrono>
struct Random {
private:
// Use xoshiro256**
// Refereces: http://xoshiro.di.unimi.it/xoshiro256starstar.c
static uint64_t rotl(const uint64_t x, int k) {
return (x << k) | (x >> (64 - k));
}
std::array<uint64_t, 4> s;
uint64_t next() {
const uint64_t result_starstar = rotl(s[1] * 5, 7) * 9;
const uint64_t t = s[1] << 17;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 45);
return result_starstar;
}
// random choice from [0, upper]
uint64_t next(uint64_t upper) {
if (!(upper & (upper + 1))) {
// b = 00..0011..11
return next() & upper;
}
int lg = 63 - __builtin_clzll(upper);
uint64_t mask = (lg == 63) ? ~0ULL : (1ULL << (lg + 1)) - 1;
while (true) {
uint64_t r = next() & mask;
if (r <= upper)
return r;
}
}
public:
Random(uint64_t seed = 0) {
// Use splitmix64
// Reference: http://xoshiro.di.unimi.it/splitmix64.c
for (int i = 0; i < 4; i++) {
uint64_t z = (seed += 0x9e3779b97f4a7c15);
z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
s[i] = z ^ (z >> 31);
}
}
// random choice from [lower, upper]
template <class T>
T uniform(T lower, T upper) {
assert(lower <= upper);
return T(lower + next(uint64_t(upper - lower)));
}
bool uniform_bool() { return uniform(0, 1) == 1; }
double uniform01() {
uint64_t v = next(1ULL << 63);
return double(v) / (1ULL << 63);
}
// generate random lower string that length = n
std::string lower_string(size_t n) {
std::string res = "";
for (size_t i = 0; i < n; i++) {
res += uniform('a', 'z');
}
return res;
}
// random shuffle
template <class Iter>
void shuffle(Iter first, Iter last) {
if (first == last) return;
// Reference and edit:
// cpprefjp - C++日本語リファレンス
// (https://cpprefjp.github.io/reference/algorithm/shuffle.html)
int len = 1;
for (auto it = first + 1; it != last; it++) {
len++;
int j = uniform(0, len - 1);
if (j != len - 1)
iter_swap(it, first + j);
}
}
// generate random permutation that length = n
template <class T>
std::vector<T> perm(size_t n) {
std::vector<T> idx(n);
std::iota(idx.begin(), idx.end(), T(0));
shuffle(idx.begin(), idx.end());
return idx;
}
template <class T>
std::vector<T> choice(size_t n, T lower, T upper) {
assert(n <= upper - lower + 1);
std::set<T> res;
while (res.size() < n) res.insert(uniform(lower, upper));
return {res.begin(), res.end()};
}
} global_gen;
Random get_random_gen() {
return Random(chrono::steady_clock::now().time_since_epoch().count());
}
template <class D> struct Poly {
V<D> v;
Poly(const V<D>& _v = {}) : v(_v) { shrink(); }
void shrink() {
while (v.size() && !v.back()) v.pop_back();
}
int size() const { return int(v.size()); }
D freq(int p) const { return (p < size()) ? v[p] : D(0); }
Poly operator+(const Poly& r) const {
auto n = max(size(), r.size());
V<D> res(n);
for (int i = 0; i < n; i++) res[i] = freq(i) + r.freq(i);
return res;
}
Poly operator-(const Poly& r) const {
int n = max(size(), r.size());
V<D> res(n);
for (int i = 0; i < n; i++) res[i] = freq(i) - r.freq(i);
return res;
}
Poly operator*(const Poly& r) const { return {multiply(v, r.v)}; }
Poly operator*(const D& r) const {
int n = size();
V<D> res(n);
for (int i = 0; i < n; i++) res[i] = v[i] * r;
return res;
}
Poly operator/(const D &r) const{
return *this * r.inv();
}
Poly operator/(const Poly& r) const {
if (size() < r.size()) return {{}};
int n = size() - r.size() + 1;
return (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
}
Poly operator%(const Poly& r) const { return *this - *this / r * r; }
Poly operator<<(int s) const {
V<D> res(size() + s);
for (int i = 0; i < size(); i++) res[i + s] = v[i];
return res;
}
Poly operator>>(int s) const {
if (size() <= s) return Poly();
V<D> res(size() - s);
for (int i = 0; i < size() - s; i++) res[i] = v[i + s];
return res;
}
Poly& operator+=(const Poly& r) { return *this = *this + r; }
Poly& operator-=(const Poly& r) { return *this = *this - r; }
Poly& operator*=(const Poly& r) { return *this = *this * r; }
Poly& operator*=(const D& r) { return *this = *this * r; }
Poly& operator/=(const Poly& r) { return *this = *this / r; }
Poly& operator/=(const D &r) {return *this = *this/r;}
Poly& operator%=(const Poly& r) { return *this = *this % r; }
Poly& operator<<=(const size_t& n) { return *this = *this << n; }
Poly& operator>>=(const size_t& n) { return *this = *this >> n; }
Poly pre(int le) const {
return {{v.begin(), v.begin() + min(size(), le)}};
}
Poly rev(int n = -1) const {
V<D> res = v;
if (n != -1) res.resize(n);
reverse(res.begin(), res.end());
return res;
}
Poly diff() const {
V<D> res(max(0, size() - 1));
for (int i = 1; i < size(); i++) res[i - 1] = freq(i) * i;
return res;
}
Poly inte() const {
V<D> res(size() + 1);
for (int i = 0; i < size(); i++) res[i + 1] = freq(i) / (i + 1);
return res;
}
// f * f.inv() = 1 + g(x)x^m
Poly inv(int m) const {
Poly res = Poly({D(1) / freq(0)});
for (int i = 1; i < m; i *= 2) {
res = (res * D(2) - res * res * pre(2 * i)).pre(2 * i);
}
return res.pre(m);
}
Poly exp(int n) const {
assert(freq(0) == 0);
Poly f({1}), g({1});
for (int i = 1; i < n; i *= 2) {
g = (g * 2 - f * g * g).pre(i);
Poly q = diff().pre(i - 1);
Poly w = (q + g * (f.diff() - f * q)).pre(2 * i - 1);
f = (f + f * (*this - w.inte()).pre(2 * i)).pre(2 * i);
}
return f.pre(n);
}
Poly log(int n) const {
assert(freq(0) == 1);
auto f = pre(n);
return (f.diff() * f.inv(n - 1)).pre(n - 1).inte();
}
Poly sqrt(int n) const {
assert(freq(0) == 1);
Poly f = pre(n + 1);
Poly g({1});
for (int i = 1; i < n; i *= 2) {
g = (g + f.pre(2 * i) * g.inv(2 * i)) / 2;
}
return g.pre(n + 1);
}
Poly pow_mod(ll n, const Poly& mod) {
Poly x = *this, r = {{1}};
while (n) {
if (n & 1) r = r * x % mod;
x = x * x % mod;
n >>= 1;
}
return r;
}
friend ostream& operator<<(ostream& os, const Poly& p) {
if (p.size() == 0) return os << "0";
for (auto i = 0; i < p.size(); i++) {
if (p.v[i]) {
os << p.v[i] << "x^" << i;
if (i != p.size() - 1) os << "+";
}
}
return os;
}
};
template <class Mint> struct MultiEval {
using NP = MultiEval*;
NP l, r;
V<Mint> que;
int sz;
Poly<Mint> mul;
MultiEval(const V<Mint>& _que, int off, int _sz) : sz(_sz) {
if (sz <= 100) {
que = {_que.begin() + off, _que.begin() + off + sz};
mul = {{1}};
for (auto x : que) mul *= {{-x, 1}};
return;
}
l = new MultiEval(_que, off, sz / 2);
r = new MultiEval(_que, off + sz / 2, sz - sz / 2);
mul = l->mul * r->mul;
}
MultiEval(const V<Mint>& _que) : MultiEval(_que, 0, int(_que.size())) {}
void query(const Poly<Mint>& _pol, V<Mint>& res) const {
if (sz <= 100) {
for (auto x : que) {
Mint sm = 0, base = 1;
for (int i = 0; i < _pol.size(); i++) {
sm += base * _pol.freq(i);
base *= x;
}
res.push_back(sm);
}
return;
}
auto pol = _pol % mul;
l->query(pol, res);
r->query(pol, res);
}
V<Mint> query(const Poly<Mint>& pol) const {
V<Mint> res;
query(pol, res);
return res;
}
};
template <class Mint> Poly<Mint> berlekamp_massey(const V<Mint>& s) {
int n = int(s.size());
V<Mint> b = {Mint(-1)}, c = {Mint(-1)};
Mint y = Mint(1);
for (int ed = 1; ed <= n; ed++) {
int l = int(c.size()), m = int(b.size());
Mint x = 0;
for (int i = 0; i < l; i++) {
x += c[i] * s[ed - l + i];
}
b.push_back(0);
m++;
if (!x) continue;
Mint freq = x / y;
if (l < m) {
// use b
auto tmp = c;
c.insert(begin(c), m - l, Mint(0));
for (int i = 0; i < m; i++) {
c[m - 1 - i] -= freq * b[m - 1 - i];
}
b = tmp;
y = x;
} else {
// use c
for (int i = 0; i < m; i++) {
c[l - 1 - i] -= freq * b[m - 1 - i];
}
}
}
return c;
}
template <class E, class Mint = decltype(E().f)>
Mint sparse_det(const VV<E>& g) {
int n = int(g.size());
if (n == 0) return 1;
auto rand_v = [&]() {
V<Mint> res(n);
for (int i = 0; i < n; i++) {
res[i] = Mint(global_gen.uniform<int>(1, Mint(-1).v));
}
return res;
};
V<Mint> c = rand_v(), l = rand_v(), r = rand_v();
// l * mat * r
V<Mint> buf(2 * n);
for (int fe = 0; fe < 2 * n; fe++) {
for (int i = 0; i < n; i++) {
buf[fe] += l[i] * r[i];
}
for (int i = 0; i < n; i++) {
r[i] *= c[i];
}
V<Mint> tmp(n);
for (int i = 0; i < n; i++) {
for (auto e : g[i]) {
tmp[i] += r[e.to] * e.f;
}
}
r = tmp;
}
auto u = berlekamp_massey(buf);
if (u.size() != n + 1) return sparse_det(g);
auto acdet = u.freq(0) * Mint(-1);
if (n % 2) acdet *= Mint(-1);
if (!acdet) return 0;
Mint cdet = 1;
for (int i = 0; i < n; i++) cdet *= c[i];
return acdet / cdet;
}
using MPol = Poly<Mint>;
Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);
int main() {
assert(i_mod * i_mod == Mint(-1));
// h(m) = 1, 1, -1, -1, 1, 1, -1, -1, ...
// f(x) = sum_{j = 1} (j + 1) x^j
// g(x) = sum_{i = 0}^{N} h(i) * f(x)^i * C(N, i) * (N - i)!
// = N! sum_{i = 0}^{N} h(i) * f(x)^i / i!
// = N! sum_{i = 0} h(i) * f(x)^i / i! (because f(0) == 0)
// g(x) / N! = sin(f(x)) + cos(f(x))
// 2i * sin(f(x)) = e^(i f(x)) - e^(- i f(x))
// 2 * cos(f(x)) = e^(i f(x)) + e^(- i f(x))
int N;
sc.read(N);
Comb<Mint> C(N + 10);
V<Mint> _f(N + 1);
for (int i = 1; i <= N; i++) {
_f[i] = Mint(i + 1) * Mint(i + 1);
}
auto f = MPol(_f);
auto ei = (f * i_mod).exp(N + 1); // e^(i f(x))
auto eni = (f * -i_mod).exp(N + 1); // e^(- i f(x))
auto sinx = (ei - eni) / (Mint(2) * i_mod);
auto cosx = (ei + eni) / Mint(2);
auto g = sinx + cosx;
/*MPol g;
for (int i = 0; i <= N; i++) {
Mint h = (i % 4 < 2 ? Mint(1) : Mint(-1));
MPol f2 = MPol({1, 0});
for (int j = 0; j < i; j++) {
f2 *= f;
}
f2 = f2.pre(N + 1);
dbg(i, f2);
g += f2 * h * C.ifact[i];
}*/
g *= C.fact[N];
;
for (int i = 1; i <= N; i++) {
pr.writeln(g.freq(i).v);
}
return 0;
}