結果
| 問題 | No.1116 Cycles of Dense Graph |
| ユーザー |
 NyaanNyaan
|
| 提出日時 | 2020-07-17 22:17:51 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 321 ms / 2,000 ms |
| コード長 | 25,091 bytes |
| コンパイル時間 | 4,780 ms |
| コンパイル使用メモリ | 260,020 KB |
| 実行使用メモリ | 4,388 KB |
| 最終ジャッジ日時 | 2023-08-20 01:44:54 |
| 合計ジャッジ時間 | 7,754 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge11 |
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 | 1 ms
4,380 KB |
| testcase_01 | AC | 176 ms
4,380 KB |
| testcase_02 | AC | 4 ms
4,380 KB |
| testcase_03 | AC | 2 ms
4,380 KB |
| testcase_04 | AC | 2 ms
4,380 KB |
| testcase_05 | AC | 8 ms
4,380 KB |
| testcase_06 | AC | 61 ms
4,380 KB |
| testcase_07 | AC | 4 ms
4,380 KB |
| testcase_08 | AC | 2 ms
4,376 KB |
| testcase_09 | AC | 2 ms
4,380 KB |
| testcase_10 | AC | 2 ms
4,380 KB |
| testcase_11 | AC | 29 ms
4,388 KB |
| testcase_12 | AC | 7 ms
4,376 KB |
| testcase_13 | AC | 2 ms
4,376 KB |
| testcase_14 | AC | 2 ms
4,384 KB |
| testcase_15 | AC | 2 ms
4,384 KB |
| testcase_16 | AC | 7 ms
4,380 KB |
| testcase_17 | AC | 2 ms
4,376 KB |
| testcase_18 | AC | 3 ms
4,380 KB |
| testcase_19 | AC | 12 ms
4,380 KB |
| testcase_20 | AC | 3 ms
4,380 KB |
| testcase_21 | AC | 3 ms
4,376 KB |
| testcase_22 | AC | 28 ms
4,376 KB |
| testcase_23 | AC | 2 ms
4,380 KB |
| testcase_24 | AC | 311 ms
4,376 KB |
| testcase_25 | AC | 2 ms
4,376 KB |
| testcase_26 | AC | 288 ms
4,376 KB |
| testcase_27 | AC | 2 ms
4,380 KB |
| testcase_28 | AC | 3 ms
4,376 KB |
| testcase_29 | AC | 2 ms
4,380 KB |
| testcase_30 | AC | 1 ms
4,380 KB |
| testcase_31 | AC | 1 ms
4,380 KB |
| testcase_32 | AC | 1 ms
4,380 KB |
| testcase_33 | AC | 1 ms
4,380 KB |
| testcase_34 | AC | 1 ms
4,376 KB |
| testcase_35 | AC | 1 ms
4,380 KB |
| testcase_36 | AC | 321 ms
4,384 KB |
| testcase_37 | AC | 76 ms
4,380 KB |
| testcase_38 | AC | 78 ms
4,380 KB |
| testcase_39 | AC | 285 ms
4,380 KB |
| testcase_40 | AC | 310 ms
4,376 KB |
ソースコード
#pragma region kyopro_template
#include <bits/stdc++.h>
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define each(x, v) for (auto &x : v)
#define all(v) (v).begin(), (v).end()
#define sz(v) ((int)(v).size())
#define mem(a, val) memset(a, val, sizeof(a))
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define inc(...) \
char __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define die(...) \
do { \
out(__VA_ARGS__); \
return; \
} while (0)
using namespace std;
using ll = long long;
template <class T>
using V = vector<T>;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vd = V<double>;
using vs = V<string>;
using vvl = vector<vector<long long>>;
using P = pair<long long, long long>;
using vp = vector<P>;
using pii = pair<int, int>;
using vpi = vector<pair<int, int>>;
constexpr int inf = 1001001001;
constexpr long long infLL = (1LL << 61) - 1;
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T, typename U>
T ceil(T a, U b) {
return (a + b - 1) / b;
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
while (n) {
if (n & 1) ret *= x;
x *= x;
n >>= 1;
}
return ret;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U>
void out(const T &t, const U &... u) {
cout << t;
if (sizeof...(u)) cout << " ";
out(u...);
}
void solve();
#ifdef NyaanDebug
#include "NyaanDebug.h"
#define trc(...) \
do { \
cerr << #__VA_ARGS__ << " = "; \
dbg_out(__VA_ARGS__); \
} while (0)
#define trca(v, N) \
do { \
cerr << #v << " = "; \
array_out(v, N); \
} while (0)
#define trcc(v) \
do { \
cerr << #v << " = {"; \
each(x, v) { cerr << " " << x << ","; } \
cerr << "}" << endl; \
} while (0)
#else
#define trc(...)
#define trca(...)
#define trcc(...)
int main() { solve(); }
#endif
inline int popcnt(unsigned long long a) { return __builtin_popcountll(a); }
inline int lsb(unsigned long long a) { return __builtin_ctzll(a); }
inline int msb(unsigned long long a) { return 63 - __builtin_clzll(a); }
template <typename T>
inline int getbit(T a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void setbit(T &a, int i) {
a |= (1LL << i);
}
template <typename T>
inline void delbit(T &a, int i) {
a &= ~(1LL << i);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
vector<T> mkrui(const vector<T> &v) {
vector<T> ret(v.size() + 1);
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T = int>
vector<T> mkiota(int N) {
vector<T> ret(N);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T = int>
vector<T> mkinv(vector<T> &v) {
vector<T> inv(v.size());
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
#pragma endregion
constexpr int MOD = /**/ 998244353; //*/ 1000000007;
template <int mod>
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-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 inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt ret(1), mul(x);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt<mod>(t);
return (is);
}
static int get_mod() { return mod; }
};
using modint = ModInt<MOD>;
using mint = modint;
using vm = vector<mint>;
namespace FastFourierTransform {
using real = double;
struct C {
real x, y;
C() : x(0), y(0) {}
C(real x, real y) : x(x), y(y) {}
inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }
inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }
inline C operator*(const C &c) const {
return C(x * c.x - y * c.y, x * c.y + y * c.x);
}
inline C conj() const { return C(x, -y); }
};
const real PI = acosl(-1);
int base = 1;
vector<C> rts = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
void ensure_base(int nbase) {
if (nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
while (base < nbase) {
real angle = PI * 2.0 / (1 << (base + 1));
for (int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
real angle_i = angle * (2 * i + 1 - (1 << base));
rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
}
++base;
}
}
void fft(vector<C> &a, int n) {
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
C z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
vector<int64_t> multiply(const vector<int> &a, const vector<int> &b) {
int need = (int)a.size() + (int)b.size() - 1;
int nbase = 1;
while ((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
vector<C> fa(sz);
for (int i = 0; i < sz; i++) {
int x = (i < (int)a.size() ? a[i] : 0);
int y = (i < (int)b.size() ? b[i] : 0);
fa[i] = C(x, y);
}
fft(fa, sz);
C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
for (int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
fa[i] = z;
}
for (int i = 0; i < (sz >> 1); i++) {
C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
fa[i] = A0 + A1 * s;
}
fft(fa, sz >> 1);
vector<int64_t> ret(need);
for (int i = 0; i < need; i++) {
ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
}
return ret;
}
}; // namespace FastFourierTransform
template <typename T>
struct ArbitraryModConvolution {
using real = FastFourierTransform::real;
using C = FastFourierTransform::C;
ArbitraryModConvolution() = default;
vector<T> multiply(const vector<T> &a, const vector<T> &b, int need = -1) {
if (need == -1) need = a.size() + b.size() - 1;
int nbase = 0;
while ((1 << nbase) < need) nbase++;
FastFourierTransform::ensure_base(nbase);
int sz = 1 << nbase;
vector<C> fa(sz);
for (int i = 0; i < (int)a.size(); i++) {
fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
}
fft(fa, sz);
vector<C> fb(sz);
if (a == b) {
fb = fa;
} else {
for (int i = 0; i < (int)b.size(); i++) {
fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
}
fft(fb, sz);
}
real ratio = 0.25 / sz;
C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
for (int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C a1 = (fa[i] + fa[j].conj());
C a2 = (fa[i] - fa[j].conj()) * r2;
C b1 = (fb[i] + fb[j].conj()) * r3;
C b2 = (fb[i] - fb[j].conj()) * r4;
if (i != j) {
C c1 = (fa[j] + fa[i].conj());
C c2 = (fa[j] - fa[i].conj()) * r2;
C d1 = (fb[j] + fb[i].conj()) * r3;
C d2 = (fb[j] - fb[i].conj()) * r4;
fa[i] = c1 * d1 + c2 * d2 * r5;
fb[i] = c1 * d2 + c2 * d1;
}
fa[j] = a1 * b1 + a2 * b2 * r5;
fb[j] = a1 * b2 + a2 * b1;
}
fft(fa, sz);
fft(fb, sz);
vector<T> ret(need);
for (int i = 0; i < need; i++) {
int64_t aa = llround(fa[i].x);
int64_t bb = llround(fb[i].x);
int64_t cc = llround(fa[i].y);
aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
ret[i] = aa + (bb << 15) + (cc << 30);
}
return ret;
}
};
template <int mod>
struct NumberTheoreticTransform {
int base, max_base, root;
vector<int> rev, rts;
NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} {
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while (tmp % 2 == 0) tmp >>= 1, max_base++;
root = 2;
while (mod_pow(root, (mod - 1) >> 1) == 1) ++root;
assert(mod_pow(root, mod - 1) == 1);
root = mod_pow(root, (mod - 1) >> max_base);
}
inline int mod_pow(int x, int n) {
int ret = 1;
while (n > 0) {
if (n & 1) ret = mul(ret, x);
x = mul(x, x);
n >>= 1;
}
return ret;
}
inline int inverse(int x) { return mod_pow(x, mod - 2); }
inline unsigned add(unsigned x, unsigned y) {
x += y;
if (x >= mod) x -= mod;
return x;
}
inline unsigned mul(unsigned a, unsigned b) {
return 1ull * a * b % (unsigned long long)mod;
}
void ensure_base(int nbase) {
if (nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
assert(nbase <= max_base);
while (base < nbase) {
int z = mod_pow(root, 1 << (max_base - 1 - base));
for (int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
rts[(i << 1) + 1] = mul(rts[i], z);
}
++base;
}
}
void ntt(vector<int> &a) {
const int n = (int)a.size();
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
int z = mul(a[i + j + k], rts[j + k]);
a[i + j + k] = add(a[i + j], mod - z);
a[i + j] = add(a[i + j], z);
}
}
}
}
vector<int> multiply(vector<int> a, vector<int> b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while ((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz, 0);
b.resize(sz, 0);
ntt(a);
ntt(b);
int inv_sz = inverse(sz);
for (int i = 0; i < sz; i++) {
a[i] = mul(a[i], mul(b[i], inv_sz));
}
reverse(a.begin() + 1, a.end());
ntt(a);
a.resize(need);
return a;
}
vector<modint> multiply_for_fps(const vector<modint> &a,
const vector<modint> &b) {
vector<int> A(a.size()), B(b.size());
for (int i = 0; i < (int)a.size(); i++) A[i] = a[i].x;
for (int i = 0; i < (int)b.size(); i++) B[i] = b[i].x;
auto C = multiply(A, B);
vector<modint> ret(C.size());
for (int i = 0; i < (int)C.size(); i++) ret[i].x = C[i];
return ret;
}
};
template <typename T>
struct FormalPowerSeries : vector<T> {
using vector<T>::vector;
using P = FormalPowerSeries;
using MULT = function<P(P, P)>;
static MULT &get_mult() {
static MULT mult = nullptr;
return mult;
}
static void set_fft(MULT f) { get_mult() = f; }
void shrink() {
while (this->size() && this->back() == T(0)) this->pop_back();
}
P operator+(const P &r) const { return P(*this) += r; }
P operator+(const T &v) const { return P(*this) += v; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator-(const T &v) const { return P(*this) -= v; }
P operator*(const P &r) const { return P(*this) *= r; }
P operator*(const T &v) const { return P(*this) *= v; }
P operator/(const P &r) const { return P(*this) /= r; }
P operator%(const P &r) const { return P(*this) %= r; }
P &operator+=(const P &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
return *this;
}
P &operator+=(const T &r) {
if (this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
P &operator-=(const P &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
shrink();
return *this;
}
P &operator-=(const T &r) {
if (this->empty()) this->resize(1);
(*this)[0] -= r;
shrink();
return *this;
}
P &operator*=(const T &v) {
const int n = (int)this->size();
for (int k = 0; k < n; k++) (*this)[k] *= v;
return *this;
}
P &operator*=(const P &r) {
if (this->empty() || r.empty()) {
this->clear();
return *this;
}
assert(get_mult() != nullptr);
return *this = get_mult()(*this, r);
}
P &operator%=(const P &r) { return *this -= *this / r * r; }
P operator-() const {
P ret(this->size());
for (int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
P &operator/=(const P &r) {
if (this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
}
P pre(int sz) const {
return P(begin(*this), begin(*this) + min((int)this->size(), sz));
}
P operator>>(int sz) const {
if (this->size() <= sz) return {};
P ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
P operator<<(int sz) const {
P ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
P rev(int deg = -1) const {
P ret(*this);
if (deg != -1) ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
P diff() const {
const int n = (int)this->size();
P ret(max(0, n - 1));
for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
return ret;
}
P integral() const {
const int n = (int)this->size();
P ret(n + 1);
ret[0] = T(0);
for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
return ret;
}
// F(0) must not be 0
P inv(int deg = -1) const {
assert(((*this)[0]) != T(0));
const int n = (int)this->size();
if (deg == -1) deg = n;
P ret({T(1) / (*this)[0]});
for (int i = 1; i < deg; i <<= 1) {
ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
}
return ret.pre(deg);
}
// F(0) must be 1
P log(int deg = -1) const {
assert((*this)[0] == 1);
const int n = (int)this->size();
if (deg == -1) deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
P sqrt(int deg = -1) const {
const int n = (int)this->size();
if (deg == -1) deg = n;
if ((*this)[0] == T(0)) {
for (int i = 1; i < n; i++) {
if ((*this)[i] != T(0)) {
if (i & 1) return {};
if (deg - i / 2 <= 0) break;
auto ret = (*this >> i).sqrt(deg - i / 2) << (i / 2);
if (ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return P(deg, 0);
}
P ret({T(1)});
T inv2 = T(1) / T(2);
for (int i = 1; i < deg; i <<= 1) {
ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
}
return ret.pre(deg);
}
// F(0) must be 0
P exp(int deg = -1) const {
assert((*this)[0] == T(0));
const int n = (int)this->size();
if (deg == -1) deg = n;
P ret({T(1)});
for (int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
P pow(int64_t k, int deg = -1) const {
const int n = (int)this->size();
if (deg == -1) deg = n;
for (int i = 0; i < n; i++) {
if ((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P C(*this * rev);
P D(n - i);
for (int j = i; j < n; j++) D[j - i] = C[j];
D = (D.log() * k).exp() * (*this)[i].pow(k);
P E(deg);
if (i * k > deg) return E;
auto S = i * k;
for (int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j];
return E;
}
}
return *this;
}
T eval(T x) const {
T r = 0, w = 1;
for (auto &v : *this) {
r += w * v;
w *= x;
}
return r;
}
};
using FPS = FormalPowerSeries<modint>;
// fにa * x^n + bを掛ける
void mul_simple(FPS &f, modint a, int n, modint b) {
for (int i = (int)f.size() - 1; i >= 0; i--) {
f[i] *= b;
if (i >= n) f[i] += f[i - n] * a;
}
}
// fからa * x^n + bを割る
void div_simple(FPS &f, modint a, int n, modint b) {
for (int i = 0; i < (int)f.size(); i++) {
f[i] /= b;
if (i + n < (int)f.size()) f[n + i] -= f[i] * a;
}
}
// f / gをdeg(f)次まで求める
FPS div_(FPS &f, FPS g) {
int n = f.size();
return (f * g.inv(n)).pre(n);
}
modint kitamasa(ll N, FPS &Q, FPS &a) {
int k = Q.size() - 1;
assert((int)a.size() == k);
FPS P = a * Q;
P.resize(k);
while (N) {
auto Q2 = Q;
for (int i = 1; i < (int)Q2.size(); i += 2) Q2[i].x = MOD - Q2[i].x;
auto S = P * Q2;
auto T = Q * Q2;
if (N & 1) {
for (int i = 1; i < (int)S.size(); i += 2) P[i >> 1].x = S[i].x;
for (int i = 0; i < (int)T.size(); i += 2) Q[i >> 1].x = T[i].x;
} else {
for (int i = 0; i < (int)S.size(); i += 2) P[i >> 1].x = S[i].x;
for (int i = 0; i < (int)T.size(); i += 2) Q[i >> 1].x = T[i].x;
}
N >>= 1;
}
return P[0];
}
struct DynamicUnionFind {
unordered_map<int, int> m;
DynamicUnionFind() {}
int data(int k) {
auto itk = m.find(k);
return itk == m.end() ? m[k] = -1 : itk->second;
}
int find(int k) {
int datk = data(k);
return datk < 0 ? k : m[k] = find(datk);
}
int unite(int x, int y) {
if ((x = find(x)) == (y = find(y))) return false;
auto itx = m.find(x), ity = m.find(y);
if (itx->second > ity->second) {
ity->second += itx->second;
itx->second = y;
} else {
itx->second += ity->second;
ity->second = x;
}
return true;
}
int size(int k) { return -data(find(k)); }
int same(int x, int y) { return find(x) == find(y); }
};
vector<ll> fac, finv, inv;
void cominit(int MAX) {
MAX++;
fac.resize(MAX, 0);
finv.resize(MAX, 0);
inv.resize(MAX, 0);
fac[0] = fac[1] = finv[0] = finv[1] = inv[1] = 1;
for (int i = 2; i < MAX; i++) {
fac[i] = fac[i - 1] * i % MOD;
inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
finv[i] = finv[i - 1] * inv[i] % MOD;
}
}
// nCk combination
inline long long COM(int n, int k) {
if (n < k || k < 0 || n < 0)
return 0;
else
return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
// nPk permutation
inline long long PER(int n, int k) {
if (n < k || k < 0 || n < 0)
return 0;
else
return (fac[n] * finv[n - k]) % MOD;
}
// nHk homogeneous polynomial
inline long long HGP(int n, int k) {
if (n == 0 && k == 0)
return 1; // depending on problem?
else if (n < 1 || k < 0)
return 0;
else
return fac[n + k - 1] * (finv[k] * finv[n - 1] % MOD) % MOD;
}
void solve() {
NumberTheoreticTransform<MOD> ntt;
auto mul = [&](const FPS::P &a, const FPS::P &b) {
auto ret = ntt.multiply_for_fps(a, b);
return FPS::P(ret.begin(), ret.end());
};
FPS::set_fft(mul);
ini(N, M);
vp e(M);
in(e);
each(p, e) p.first--, p.second--;
DynamicUnionFind uf;
unordered_map<int, int> m;
cominit(N * 2 + 100);
map<P, mint> memo;
mint ans = 0;
// houzyo
rep(b, 1 << M) {
uf.m.clear();
m.clear();
vi ps;
rep(i, M) {
if (!getbit(b, i)) continue;
m[e[i].first]++, m[e[i].second]++;
uf.unite(e[i].first, e[i].second);
ps.pb(e[i].first);
ps.pb(e[i].second);
}
int flg = 0;
each(x, m) if (x.second >= 3) flg = 1;
if (flg) continue;
ps = mkuni(ps);
vi used(sz(ps));
// 連結成分ごとにアをする めんどいな
int cycle = 0, notcycle = 0, dec = 0;
rep(i, sz(ps)) {
if (used[i]) continue;
// 同じ連結成分は？
vi p{ps[i]};
used[i] = 1;
for (int j = i + 1; j < sz(ps); j++)
if (uf.same(ps[i], ps[j])) p.pb(ps[j]), used[j] = 1;
// saikuru?
assert(p.size()==uf.size(p.back()));
int all2 = 1;
each(x, p) if (m[x] != 2) all2 = 0;
if (all2)
cycle += 1;
else
notcycle += 1, dec += sz(p);
}
mint coeff = popcnt(b) % 2 == 0 ? 1 : -1;
if (cycle >= 2 or (cycle == 1 and notcycle)) continue;
if (cycle == 1) {
ans += coeff;
continue;
}
// soreigai
// 絶対使う向きつき頂点 notcycle個
// 使わなくてもいい点 N-dec個
trc(cycle, notcycle, dec);
// 1ko mukikotei
mint cur = 1;
if (notcycle >= 2) cur *= mint(2).pow(notcycle - 1) * fac[notcycle - 1];
// soreigai ireru
int M = N - dec;
//
// 1ko
// hazimeha notcycle
// i ko tukau
// no * (no+1) * ... * (no + i - 1) * NCi
// koreha? 1st starling?
if (memo.find(P{notcycle, dec}) != memo.end()) {
cur *= memo[P{notcycle, dec}];
} else {
mint x = 0;
if (notcycle == 0) {
// N choten
for (int i = 3; i <= N; i++) {
x += mint(COM(N, i)) * mint(fac[i - 1]) / 2;
}
} else {
for (int i = 0; i <= M; i++) {
if (dec == 2 and i == 0)
continue;
else
x += mint(COM(M, i)) * fac[notcycle + i - 1] * finv[notcycle - 1];
}
}
memo[P{notcycle, dec}] = x;
cur *= x;
}
ans += cur * coeff;
}
out(ans);
}