test/yukicoder/2507.test.cpp

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• Last update: 2025-08-12 22:13:25+09:00
• Problem: https://yukicoder.me/problems/no/2507

Depends on

• 無向グラフ数え上げ(集合冪級数) (src/Graph/UndirectedGraphSetPowerSeries.hpp)
• 集合冪級数 (src/Math/set_power_series.hpp)

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/2507
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include "src/Graph/UndirectedGraphSetPowerSeries.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int n, m;
 cin >> n >> m;
 UndirectedGraphSetPowerSeries g(n);
 for (int i= 0, u, v; i < m; ++i) cin >> u >> v, g.add_edge(--u, --v);
 auto f= g.cycle_graph<long long>();
 for (int i= n; i--;) f[1 << i]= 1;
 cout << g.disjoint_union(g.bridge_union(f)).back() << '\n';
 return 0;
}

#line 1 "test/yukicoder/2507.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/2507
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#line 2 "src/Math/set_power_series.hpp"
#include <algorithm>
#include <vector>
#include <cassert>
#include <cstdint>
namespace sps {
namespace _sps_internal {
using namespace std;
#define _ZETA(s, l) \
 if constexpr (!t) A[s + l]+= A[s]; \
 else if constexpr (t == 1) A[s + l]-= A[s]; \
 else if constexpr (t == 2) A[s]+= A[s + l]; \
 else if constexpr (t == 3) A[s]-= A[s + l]; \
 else tie(A[s], A[s + l])= make_pair(A[s] + A[s + l], A[s] - A[s + l]);
template <int t, class T> void rec(T A[], int l) {
 if (l > 127) {
  l>>= 1, rec<t>(A, l), rec<t>(A + l, l);
  for (int s= 0; s < l; ++s) _ZETA(s, l);
 } else
  for (int k= 1; k < l; k<<= 1)
   for (int i= 0; i < l; i+= k + k)
    for (int j= 0; j < k; ++j) _ZETA(i + j, k);
}
#undef _ZETA
/*  f -> g s.t. g[S] = sum_{T subseteq S} f[T]  O(n 2^n) */
template <class T> void subset_zeta(vector<T>& f) { rec<0>(f.data(), f.size()); }
/*  f -> h s.t. f[S] = sum_{T subseteq S} h[T]  O(n 2^n) */
template <class T> void subset_mobius(vector<T>& f) { rec<1>(f.data(), f.size()); }
/*  f -> g s.t. g[S] = sum_{S subseteq T} f[T]  O(n 2^n) */
template <class T> void supset_zeta(vector<T>& f) { rec<2>(f.data(), f.size()); }
/*  f -> h s.t. f[S] = sum_{S subseteq T} h[T]  O(n 2^n) */
template <class T> void supset_mobius(vector<T>& f) { rec<3>(f.data(), f.size()); }
/* h[S] = sum_{U | T == S} f[U]g[T]  O(n 2^n) */
template <class T> vector<T> or_convolve(vector<T> f, vector<T> g) {
 subset_zeta(f), subset_zeta(g);
 for (int s= f.size(); s--;) f[s]*= g[s];
 return subset_mobius(f), f;
}
/* h[S] = sum_{U & T == S} f[U]g[T]  O(n 2^n) */
template <class T> vector<T> and_convolve(vector<T> f, vector<T> g) {
 supset_zeta(f), supset_zeta(g);
 for (int s= f.size(); s--;) f[s]*= g[s];
 return supset_mobius(f), f;
}
/* f -> g s.t. g[S] = sum_{T} (-1)^{|S & T|} f[T] */
template <class T> void hadamard(vector<T>& f) { rec<4>(f.data(), f.size()); }
/* h[S] = sum_{U ^ T = S} f[U]g[T] */
template <class T> vector<T> xor_convolve(vector<T> f, vector<T> g) {
 hadamard(f), hadamard(g);
 for (int s= f.size(); s--;) f[s]*= g[s];
 hadamard(f);
 if (T iv= T(1) / f.size(); iv == 0)
  for (int s= f.size(); s--;) f[s]/= f.size();
 else
  for (int s= f.size(); s--;) f[s]*= iv;
 return f;
}
template <int t, class T> void rec_r(T A[], int l, int n, int c= 0) {
 if (l >= (n << 4)) {
  l>>= 1, rec_r<t>(A, l, n, c), rec_r<t>(A + l, l, n, c + 1);
  for (int s= l / n; s--;)
   if constexpr (!t)
    for (int d= 0, e= __builtin_popcount(s) + c + 1; d < e; ++d) A[s * n + d + l]+= A[s * n + d];
   else
    for (int d= __builtin_popcount(s) + c + 1; d < n; ++d) A[s * n + d + l]-= A[s * n + d];
 } else
  for (int k= 1, m= l / n; k < m; k<<= 1)
   for (int i= 0; i < m; i+= k + k)
    for (int j= 0; j < k; ++j)
     if constexpr (!t)
      for (int u= i + j, s= u + k, d= 0, e= __builtin_popcount(s) + c; d < e; ++d) A[s * n + d]+= A[u * n + d];
     else
      for (int u= i + j, s= u + k, d= __builtin_popcount(s) + c; d < n; ++d) A[s * n + d]-= A[u * n + d];
}
template <class T> void rnk_zeta(const T f[], T F[], int n) {
 for (int s= 1 << n; s--;) F[s * (n + 1) + __builtin_popcount(s)]= f[s];
 rec_r<0>(F, (n + 1) << n, n + 1);
}
template <class T> void rnk_mobius(T F[], T f[], int n) {
 rec_r<1>(F, (n + 1) << n, n + 1);
 for (int s= 1 << n; s--;) f[s]= F[s * (n + 1) + __builtin_popcount(s)];
}
template <class T> void cnv_(T A[], T B[], int n) {
 for (int s= 1 << (n - 1); s--;) {
  T t, *a= A + s * n, *b= B + s * n;
  for (int c= __builtin_popcount(s), d= min(2 * c, n - 1), e; d >= c; a[d--]= t)
   for (t= 0, e= d - c; e <= c; ++e) t+= a[e] * b[d - e];
 }
}
template <class T> void cnv_na(const T f[], const T g[], T h[], int N) {
 for (int s= N, t; s--;)
  for (h[t= s]= f[s] * g[0]; t; --t&= s) h[s]+= f[s ^ t] * g[t];
}
// fg, O(n^2 2^n)
template <class T> vector<T> convolve(const vector<T>& f, const vector<T>& g) {
 const int N= f.size(), n= __builtin_ctz(N);
 assert(!(N & (N - 1))), assert(N == (int)g.size());
 vector<T> h(N);
 if (n < 11) return cnv_na(f.data(), g.data(), h.data(), N), h;
 vector<T> F((n + 1) << n);
 if (rnk_zeta(f.data(), F.data(), n); f.data() == g.data()) return cnv_(F.data(), F.data(), n + 1), rnk_mobius(F.data(), h.data(), n), h;
 vector<T> G((n + 1) << n);
 return rnk_zeta(g.data(), G.data(), n), cnv_(F.data(), G.data(), n + 1), rnk_mobius(F.data(), h.data(), n), h;
}
template <class T> void div_na(T f[], const T g[], int N) {
 for (int s= 1; s < N; ++s)
  for (int t= s; t; --t&= s) f[s]-= f[s ^ t] * g[t];
}
// 1/f, "f[empty] = 1" is required, O(n^2 2^n)
template <class T> vector<T> inv(const vector<T>& f) {
 const int N= f.size(), n= __builtin_ctz(N);
 assert(!(N & (N - 1))), assert(f[0] == 1);
 vector<T> h(N);
 if (n < 11) return h[0]= 1, div_na(h.data(), f.data(), N), h;
 vector<T> F((n + 1) << n), G((n + 1) << n);
 rnk_zeta(f.data(), G.data(), n);
 for (int s= N; s--;) {
  T *a= F.data() + s * (n + 1), *b= G.data() + s * (n + 1);
  a[0]= 1;
  for (int d= 0, c= __builtin_popcount(s); d++ < n;)
   for (int e= max(0, d - c); e < d; ++e) a[d]-= a[e] * b[d - e];
 }
 return rnk_mobius(F.data(), h.data(), n), h;
}
// f/g, "f[empty] = 1" is required, O(n^2 2^n)
template <class T> vector<T> div(vector<T> f, const vector<T>& g) {
 const int N= f.size(), n= __builtin_ctz(N);
 assert(!(N & (N - 1))), assert(N == (int)g.size()), assert(g[0] == 1);
 if (n < 12) return div_na(f.data(), g.data(), N), f;
 vector<T> F((n + 1) << n), G((n + 1) << n);
 rnk_zeta(f.data(), F.data(), n), rnk_zeta(g.data(), G.data(), n);
 for (int s= N; s--;) {
  T *a= F.data() + s * (n + 1), *b= G.data() + s * (n + 1);
  for (int d= 0, c= __builtin_popcount(s); d++ < n;)
   for (int e= max(0, d - c); e < d; ++e) a[d]-= a[e] * b[d - e];
 }
 return rnk_mobius(F.data(), f.data(), n), f;
}
template <class T, class P> void oncnv_(const T f[], T h[], const P& phi, int n) {
 vector<T> F((n + 1) << n), G((n + 1) << n);
 rnk_zeta(f, F.data(), n), fill_n(G.data(), 1 << n, h[0]);
 T* a= G.data() + (1 << n);
 for (int l= 1 << n; l>>= 1;) phi(l, a[l]= h[0] * f[l]), h[l]= a[l];
 for (int d= 2, s; d <= n; ++d) {
  for (rec<0>(a, 1 << n), a+= (s= 1 << n); --s;)
   if (int c= __builtin_popcount(s); c <= d && d <= 2 * c)
    for (int e= d; e--;) a[s]+= G[e << n | s] * F[s * (n + 1) + d - e];
  for (rec<1>(a, 1 << n), s= 1 << n; --s;)
   if (__builtin_popcount(s) == d) phi(s, a[s]), h[s]= a[s];
   else a[s]= 0;
 }
}
// h[S] = phi(S, sum_{T subsetneq S} h[T]f[S/T] )  O(n^2 2^n)
// phi: [](int, T&x)
template <class T, class P> vector<T> semi_relaxed_convolve(const vector<T>& f, T init, const P& phi) {
 const int N= f.size(), n= __builtin_ctz(N);
 assert(!(N & (N - 1)));
 vector<T> h(N);
 if (h[0]= init; n < 12) {
  for (int s= 1, t; s < N; phi(s, h[s]), ++s)
   for (t= s; t; --t&= s) h[s]+= h[s ^ t] * f[t];
 } else oncnv_(f.data(), h.data(), phi, n);
 return h;
}
// h[S] = phi(S, 1/2 sum_{empty neq T subseteq S} h[T]h[S/T] )  O(n^2 2^n)
// phi: [](int, T&x)
template <class T, class P> vector<T> self_relaxed_convolve(const P& phi, int n) {
 const int e= min(n, 12);
 int i= 0, l= 1;
 vector<T> f(1 << n);
 for (int u= 1; i < e; l<<= 1, ++i)
  for (int s= 0; s < l; phi(u, f[u]), ++s, ++u)
   for (int t= s; t; --t&= s) f[u]+= f[u ^ t] * f[t];
 for (; i < n; l<<= 1, ++i) phi(l, f[l]), oncnv_(f.data(), f.data() + l, [&](int s, T& x) { phi(s | l, x); }, i);
 return f;
}
// exp(f) , "f[empty] = 0" is required,  O(n^2 2^n)
template <class T> vector<T> exp(const vector<T>& f) {
 const int N= f.size(), n= __builtin_ctz(N), e= min(n, 11);
 assert(!(N & (N - 1))), assert(f[0] == 0);
 vector<T> h(N);
 int i= 0, l= 1;
 for (h[0]= 1; i < e; l<<= 1, ++i) cnv_na(h.data(), f.data() + l, h.data() + l, l);
 for (; i < n; l<<= 1, ++i) {
  vector<T> F((i + 1) << i), G((i + 1) << i);
  rnk_zeta(h.data(), F.data(), i), rnk_zeta(f.data() + l, G.data(), i), cnv_(F.data(), G.data(), i + 1), rnk_mobius(F.data(), h.data() + l, i);
 }
 return h;
}
// log(f) , "f[empty] = 1" is required,  O(n^2 2^n)
template <class T> vector<T> log(const vector<T>& f) {
 const int N= f.size(), n= __builtin_ctz(N), e= min(n, 12);
 assert(!(N & (N - 1))), assert(f[0] == 1);
 vector<T> h= f;
 int i= 0, l= 1;
 for (h[0]= 0; i < e; l<<= 1, ++i) div_na(h.data() + l, f.data(), l);
 if (i < n) {
  vector<T> G(n << (n - 1));
  rnk_zeta(f.data(), G.data(), n - 1);
  for (; i < n; l<<= 1, ++i) {
   vector<T> F((i + 1) << i, 0);
   if constexpr (is_floating_point_v<T>) {
    fill_n(F.data(), l, h[l]= f[l]);
    T* a= F.data() + l;
    for (int m= l; m>>= 1;) h[l | m]= a[m]= f[l | m] - h[l] * f[m];
    for (int d= 2, s; d <= i; ++d) {
     for (rec<0>(a, l), a+= (s= l); --s;)
      if (int c= __builtin_popcount(s); c <= d && d <= 2 * c)
       for (int e= d; e--;) a[s]+= F[e << i | s] * G[s * n + d - e];
     for (rec<1>(a, l), s= l; --s;)
      if (__builtin_popcount(s) == d) h[l | s]= a[s]= f[l | s] - a[s];
      else a[s]= 0;
    }
   } else {
    rnk_zeta(f.data() + l, F.data(), i);
    for (int s= l; s--;) {
     T t, *a= F.data() + s * (i + 1), *b= G.data() + s * n;
     for (int d= 0, c= __builtin_popcount(s), e; d++ < i; a[d]-= t)
      for (t= 0, e= max(0, d - c); e < d; ++e) t+= a[e] * b[d - e];
    }
    rnk_mobius(F.data(), h.data() + l, i);
   }
  }
 }
 return h;
}
// F(f) =  sum_i F_i f^i/i! , "f[empty] = 0" is required, O(n^2 2^n)
template <class T> vector<T> egf_comp(const vector<T>& F, const vector<T>& f) {
 const int N= f.size(), n= __builtin_ctz(N), e= min(n, 11);
 assert(!(N & (N - 1))), assert(f[0] == 0);
 vector<T> h(N);
 T* b= h.data() + N;
 for (int i= n - F.size(); i++ < n;) h[N - (1 << i)]= F[n - i];
 int i= 0, l= 1;
 for (; i < e; l<<= 1, ++i)
  for (int j= N >> 1; j >= l; j>>= 1) cnv_na(b - j, f.data() + l, b - j - j + l, l);
 if (i < n) {
  vector<T> A(n << (n - 1)), B(n << (n - 1));
  for (; i < n; l<<= 1, ++i) {
   fill_n(B.data(), (i + 1) << i, 0), rnk_zeta(f.data() + l, B.data(), i);
   for (int j= N >> 1; j >= l; j>>= 1) fill_n(A.data(), (i + 1) << i, 0), rnk_zeta(b - j, A.data(), i), cnv_(A.data(), B.data(), i + 1), rnk_mobius(A.data(), b - j - j + l, i);
  }
 }
 return h;
}
// P(f) = sum_{i=0}^m P_i f^i ,  O(n^2 2^n)
template <class T> vector<T> poly_comp(vector<T> P, vector<T> f) {
 const int N= f.size(), n= __builtin_ctz(N);
 assert(!(N & (N - 1)));
 vector<T> F(n + 1);
 for (int j= 0, e= P.size();; ++j, --e) {
  for (int i= e; i--;) (F[j]*= f[0])+= P[i];
  if (j == n || e <= 1) break;
  for (int i= 1; i < e; ++i) P[i - 1]= P[i] * i;
 }
 return f[0]= 0, egf_comp(F, f);
}
// f^k ,  O(n^2 2^n)
template <class T> vector<T> pow(vector<T> f, uint64_t k) {
 const unsigned N= f.size(), n= __builtin_ctz(N);
 assert(!(N & (N - 1)));
 vector<T> F;
 unsigned i, m;
 if (n < k) {
  F.resize(n + 1), F[m= n]= 1;
  T x= f[0];
  for (uint64_t l= k - n;; x*= x)
   if (l & 1 ? F[n]*= x : 0; !(l>>= 1)) break;
 } else F.resize(k + 1), F[m= k]= 1;
 for (i= m; i--;) F[i]= F[i + 1] * f[0];
 for (T t= 1; ++i < m;) F[i + 1]*= (t*= k - i);
 return f[0]= 0, egf_comp(F, f);
}
template <class T> vector<T> _egfT(const T* b, T* h, int M, int n) {
 T *a, *d;
 vector<T> c(n + 1);
 int l= M;
 if (int i= __builtin_ctz(M); i > 10) {
  vector<T> F((i + 1) << i), G((i + 1) << i);
  for (int m, s; i > 10; fill_n(F.data(), (i + 1) << i, 0), rnk_zeta(h, F.data(), i), cnv_(F.data(), G.data(), i + 1), rnk_mobius(F.data(), h, i), b-= (l>>= 1), --i)
   for (fill_n(G.data(), (i + 1) << i, 0), rnk_zeta(b, G.data(), i), m= M; m > l; m>>= 1)
    for (a= h + (m - l), fill_n(F.data(), (i + 1) << i, 0), rnk_zeta(a + m - l, F.data(), i), cnv_(F.data(), G.data(), i + 1), rec_r<1>(F.data(), (i + 1) << i, i + 1), s= l; s--;) a[s]+= F[s * (i + 1) + __builtin_popcount(s)];
 }
 for (; l; cnv_na(h, b, h, l), b-= (l>>= 1))
  for (int m= M, s, t; m > l; m>>= 1)
   for (a= h + (m - l), d= a + (m - l), s= l; s--;)
    for (a[t= s]+= d[s] * b[0]; t; --t&= s) a[s]+= d[s ^ t] * b[t];
 for (int i= 0; i <= n; ++i) c[i]= h[(1 << (n - i)) - 1];
 return c;
}
// [X^{[n]}] f^k/k! for k=0,1,...,n , O(n^2 2^n)
template <class T> vector<T> egf_T(vector<T> f) {
 const int N= f.size(), n= __builtin_ctz(N);
 assert(!(N & (N - 1)));
 if (n == 0) return {1};
 if (n == 1) return {0, f[1]};
 return _egfT(f.data() + (N >> 2), f.data() + (N >> 1), N >> 2, n);
}
// [X^{[n]}] f^k/k! g for k=0,1,...,n , O(n^2 2^n)
template <class T> vector<T> egf_T(const vector<T>& f, vector<T> g) {
 const int N= f.size(), n= __builtin_ctz(N);
 assert(!(N & (N - 1)));
 if (n == 0) return {g[1]};
 return _egfT(f.data() + (N >> 1), g.data(), N >> 1, n);
}
}
using _sps_internal::subset_zeta, _sps_internal::subset_mobius, _sps_internal::supset_zeta, _sps_internal::supset_mobius, _sps_internal::hadamard, _sps_internal::or_convolve, _sps_internal::and_convolve, _sps_internal::xor_convolve, _sps_internal::convolve, _sps_internal::semi_relaxed_convolve, _sps_internal::self_relaxed_convolve, _sps_internal::inv, _sps_internal::div, _sps_internal::exp, _sps_internal::log, _sps_internal::egf_comp, _sps_internal::poly_comp, _sps_internal::pow, _sps_internal::egf_T;
}
#line 3 "src/Graph/UndirectedGraphSetPowerSeries.hpp"
class UndirectedGraphSetPowerSeries {
 using u64= unsigned long long;
 template <class T> using Sps= std::vector<T>;
 template <class T> using Poly= std::vector<T>;
 const int n, N, m, o;
 std::vector<u64> adj;
 std::vector<int> es;
 template <class T> static inline T pow(T x, int k) {
  for (T ret(1);; x*= x)
   if (k& 1 ? ret*= x : 0; !(k>>= 1)) return ret;
 }
 template <class F> inline void bfs(int s, const F& f) const {
  for (int t= s, u, j; t;)
   for (f(u= 1 << __builtin_ctz(t)); u;) j= __builtin_ctz(u), t^= 1 << j, u^= 1 << j, u|= es[j] & t;
 }
 template <class T, class G> static inline void transform_articulation(Sps<T>& f, const G& g) {
  const int M= f.size() / 2;
  Sps<T> tmp(M);
  for (int I= M; I; I>>= 1) {
   for (int t= 0; t < M; t+= I)
    for (int u= I, t2= t << 1; u--;) tmp[t | u]= f[t2 | I | u];
   tmp= g(tmp);
   for (int t= 0; t < M; t+= I)
    for (int u= I, t2= t << 1; u--;) f[t2 | I | u]= tmp[t | u];
  }
 }
 template <class T, bool b> inline void transform_bridge(Sps<T>& f) const {
  const int M= N / 2;
  Sps<T> tmp(M), tmp2;
  for (int i= n, I= M; --i; I>>= 1) {
   for (int t= 0; t < M; t+= I)
    for (int u= I, t2= t << 1; u--;) tmp[t | u]= f[t2 | I | u];
   tmp2.assign(M, 0);
   for (int t= 0; t < M; t+= I)
    for (int j= i, J= I, t2= t << 1; J>>= 1, j--;)
     for (int s= J, J2= J * 2; s < I; s+= J2)
      for (int u= s + J; u-- > s;) {
       if constexpr (b) tmp2[t | u]+= f[t2 | u] * adj[i * m + j];
       else tmp2[t | u]-= f[t2 | u] * adj[i * m + j];
      }
   tmp= sps::convolve(tmp, sps::exp(tmp2));
   for (int t= 0; t < M; t+= I)
    for (int u= I, t2= t << 1; u--;) f[t2 | I | u]= tmp[t | u];
  }
 }
 template <class T> inline std::vector<T> cyc() const {
  std::vector<T> cyc(1 << o);
  for (int i= 0; i < o; ++i) {
   int a= i + i, b= a + 1, K= a + 2, I= 1 << i;
   std::vector<T> dp0(K << i);
   dp0[a]= 1;
   for (int s= 0; s < I; ++s) {
    T* dp0s= dp0.data() + (s * K);
    for (int u= s | I, S= u, j, j0, j1; S; S^= 1 << j) {
     j= __builtin_ctz(S), j0= j + j, j1= j0 + 1;
     const u64 *A0= adj.data() + (j0 * m), *A1= A0 + m;
     T dp0s0= dp0s[j0], dp0s1= dp0s[j1];
     cyc[u]+= dp0s0 * A0[b] + dp0s1 * A1[b];
     for (int U= I - 1 - s, k, k0, k1; U; U^= 1 << k) {
      k= __builtin_ctz(U), k0= k + k, k1= k0 + 1;
      dp0s[(K << k) + k0]+= dp0s0 * A0[k1] + dp0s1 * A1[k1], dp0s[(K << k) + k1]+= dp0s0 * A0[k0] + dp0s1 * A1[k0];
     }
    }
   }
  }
  return cyc;
 }
 template <class T> inline std::pair<std::vector<T>, std::vector<T>> cyc_pth() const {
  std::vector<T> cyc(1 << o), pth(1 << o);
  for (int i= 0; i < o; ++i) {
   int a= i + i, b= a + 1, K= a + 2, I= 1 << i;
   std::vector<T> dp0(K << i), dp1(K << i);
   dp0[a]= 1;
   for (int s= 0; s < I; ++s) {
    T *dp0s= dp0.data() + (s * K), *dp1s= dp1.data() + (s * K);
    for (int j= 0; j < K; ++j) dp1s[b]+= dp0s[j];
    for (int u= s | I, S= u, j, j0, j1; S; S^= 1 << j) {
     j= __builtin_ctz(S), j0= j + j, j1= j0 + 1;
     const u64 *A0= adj.data() + (j0 * m), *A1= A0 + m;
     T dp0s0= dp0s[j0], dp0s1= dp0s[j1], dp1s0= dp1s[j0], dp1s1= dp1s[j1];
     cyc[u]+= dp0s0 * A0[b] + dp0s1 * A1[b], pth[u]+= dp1s0 + dp1s1;
     for (int U= I - 1 - s, k, k0, k1; U; U^= 1 << k) {
      k= __builtin_ctz(U), k0= k + k, k1= k0 + 1;
      dp0s[(K << k) + k0]+= dp0s0 * A0[k1] + dp0s1 * A1[k1], dp0s[(K << k) + k1]+= dp0s0 * A0[k0] + dp0s1 * A1[k0];
      dp1s[(K << k) + k0]+= dp1s0 * A0[k1] + dp1s1 * A1[k1], dp1s[(K << k) + k1]+= dp1s0 * A0[k0] + dp1s1 * A1[k0];
     }
    }
   }
  }
  return {cyc, pth};
 }
public:
 UndirectedGraphSetPowerSeries(int n): n(n), N(1 << n), m(n + (n & 1)), o(m / 2), adj(m * m), es(n) {}
 template <class Int> UndirectedGraphSetPowerSeries(const std::vector<std::vector<Int>>& g): n(g.size()), N(1 << n), m(n + (n & 1)), o(m / 2), adj(m * m), es(n) {
  for (int i= n; i--;)
   for (int j= i; j--;) assert(g[i][j] == g[j][i]);
  for (int i= n; i--;)
   for (int j= n; j--;) adj[i * m + j]= g[i][j];
  for (int i= n; i--;)
   for (int j= n; j--;) es[i]|= !(!(adj[i * m + j])) << j;
 }
 void add_edge(int u, int v, u64 cnt= 1) {
  adj[u * m + v]= (adj[v * m + u]+= cnt), es[u]|= (1 << v), es[v]|= (1 << u);
  if (!(adj[u * m + v])) es[u]^= (1 << v), es[v]^= (1 << u);
 }
 const auto operator[](int u) const { return adj.begin() + (u * m); }
 template <class T> static inline Sps<T> only_connected(const Sps<T>& f) { return sps::log(f); }
 template <class T> static inline Sps<T> disjoint_union(const Sps<T>& f) { return sps::exp(f); }
 template <class T> static inline Sps<T> only_biconnected(Sps<T> f) { return transform_articulation(f, sps::log<T>), f; }
 template <class T> static inline Sps<T> articulation_union(Sps<T> f) { return transform_articulation(f, sps::exp<T>), f; }
 template <class T> inline Sps<T> only_2edge_connected(Sps<T> f) const { return transform_bridge<T, false>(f), f; }
 template <class T> inline Sps<T> bridge_union(Sps<T> f) const { return transform_bridge<T, true>(f), f; }
 inline Sps<u64> edge_num() const {
  Sps<u64> ret(N, 0);
  for (int i= n; i--;)
   for (int j= i; j--;) ret[(1 << i) | (1 << j)]= adj[i * m + j];
  return sps::subset_zeta(ret), ret;
 }
 inline Sps<int> connected_component_num() const {
  Sps<int> ret(N, 0);
  for (int s= N; s--;) bfs(s, [&](int) { ret[s]++; });
  return ret;
 }
 inline Sps<u64> cycle_space_rank() const {
  Sps<u64> e= edge_num(), ret(N, 0);
  Sps<int> k= connected_component_num();
  for (int s= N; s--;) ret[s]= e[s] + k[s] - __builtin_popcount(s);
  return ret;
 }
 inline Sps<u64> odd_deg_num() const {
  Sps<u64> ret(N, 0);
  for (int i= n, I= N; I>>= 1, i--;)
   for (int t= 0, I2= I << 1; t < N; t+= I2)
    for (int u= I, cnt, v, j; u--; ret[t | I | u]+= cnt & 1)
     for (cnt= 0, v= t | u; v; v^= 1 << j) cnt+= adj[i * m + (j= __builtin_ctz(v))];
  return ret;
 }
 inline Sps<u64> selfloop_num() const {
  Sps<u64> ret(N, 0);
  for (int i= 0, I= 1; i < n; ++i, I<<= 1)
   for (int u= I; u--;) ret[I | u]= ret[u] + adj[i * m + i];
  return ret;
 }
 template <class T, class Int> static inline Sps<T> space_size(const Sps<Int>& rank) {
  Sps<T> ret(rank.size());
  for (int s= rank.size(); s--;) ret[s]= pow<T>(2, rank[s]);
  return ret;
 }
 template <class T> inline Sps<T> graph() const { return space_size<T>(edge_num()); }
 template <class T> inline Sps<T> cycle_space_size() const { return space_size<T>(cycle_space_rank()); }
 template <class T> inline Sps<T> connected_graph() const { return sps::log(graph<T>()); }
 template <class T> inline Sps<T> eulerian_graph() const { return sps::log(cycle_space_size<T>()); }
 template <class T> inline Sps<T> connected_biparate_graph() const {
  Sps<T> tmp= graph<T>(), ret(N, 1);
  for (int s= N; s--;) ret[s]/= tmp[s];
  ret= sps::convolve(ret, ret);
  for (int s= N; s--;) ret[s]*= tmp[s];
  ret= sps::log(ret);
  for (int s= N; s--;) ret[s]/= 2;
  return ret;
 }
 template <class T> inline Sps<T> tree() const {
  Sps<u64> e= edge_num();
  Sps<T> ret= {0, 1};
  ret.reserve(N);
  for (int I= 2; I < N; I<<= 1) {
   Sps<T> g(ret);
   for (int s= I; --s;) g[s]*= e[s | I] - e[s] - e[I];
   g= sps::exp(g), std::copy(g.begin(), g.end(), std::back_inserter(ret));
  }
  return ret;
 }
 template <class T> inline Sps<T> forest() const { return sps::exp(tree<T>()); }
 template <class T> inline Sps<T> cycle_graph() const {
  T dp[N][n - 1];
  Sps<T> ret(N, 0);
  for (int i= n, I= N; I>>= 1, --i;) {
   for (int s= I; --s;) std::fill_n(dp[s], i, 0);
   for (int j= i; j--;) dp[1 << j][j]= adj[i * m + j];
   for (int s= 1; s < I; ++s)
    for (int t= s, j, u, r, k; t; ret[s | I]+= dp[s][j] * adj[j * m + i])
     for (t^= 1 << (j= __builtin_ctz(t)), u= r= s ^ (1 << j); u; dp[s][j]+= dp[r][k] * adj[k * m + j]) u^= 1 << (k= __builtin_ctz(u));
  }
  for (int i= n; i--;)
   for (int j= i; j--;) ret[(1 << i) | (1 << j)]-= adj[i * m + j];
  for (int s= N; --s;) ret[s]/= 2;
  return ret;
 }
 template <class T> inline Sps<T> biconnected_graph() const {
  Sps<T> ret= connected_graph<T>();
  return transform_articulation(ret, sps::log<T>), ret;
 }
 template <class T> inline Sps<T> two_edge_connected_graph() const {
  Sps<T> ret= connected_graph<T>();
  return transform_bridge<T, false>(ret), ret;
 }
 template <class T> inline Sps<T> cactus_graph() const {
  auto ret= cycle_graph<T>();
  for (int i= n; i--;)
   for (int j= i; j--;) ret[(1 << i) | (1 << j)]+= adj[i * m + j];
  return transform_articulation(ret, sps::exp<T>), ret;
 }
 template <class T> inline Sps<T> acyclic_orientations() const {
  auto k= connected_component_num();
  Sps<T> g(N, 0);
  for (int s= N; --s;)
   if (k[s] == __builtin_popcount(s)) g[s]= k[s] & 1 ? -1 : 1;
  return g[0]= 1, sps::inv(g);
 }
 template <class T> inline std::vector<T> colorings_using_exactly_k_colors_num() const {
  if (n == 0) return {0};  // impossible in any number of ways
  auto k= connected_component_num();
  std::vector<T> indep(N, 0);
  for (int s= N; --s;) indep[s]= k[s] == __builtin_popcount(s);
  return sps::egf_T(indep);
 }
 template <class T> inline Poly<T> chromatic_polynomial() const {
  auto e= colorings_using_exactly_k_colors_num<T>();
  if (e.back() == 0) return {0};
  Poly<T> ret(n + 1, 0);
  std::vector<T> tmp(n);
  tmp[0]= 1;
  for (int i= 1, j; i < n; ++i)
   for (j= i; j--; tmp[j]*= -i) ret[j + 1]+= tmp[j] * e[i], tmp[j + 1]+= tmp[j];
  for (int j= n; j--;) ret[j + 1]+= tmp[j];
  return ret;
 }
 template <class T> inline T tutte_polynomial(T x, T y) const {
  int sum[N], s, t, lim= 2, i, j;
  T fum[10'000]= {0, 1};
  std::vector<T> g= {0}, h;
  for (g.reserve(N), h.reserve(N), i= 0; i < n; h= sps::exp(h), std::copy(h.begin(), h.end(), std::back_inserter(g)), ++i) {
   for (sum[0]= j= 0; j < i; j++)
    for (s= t= 1 << j; s--;) sum[s | t]= sum[s] + adj[i * m + j];
   for (h.resize(s= 1 << i); s--; h[s]= g[s] * fum[sum[s]])
    for (; lim <= sum[s]; lim++) fum[lim]= fum[lim - 1] * y + 1;
  }
  for (x-= 1, t= ~0, j= 0, i= n; i--;) j+= adj[i * m + i];
  for (bfs((s= N) - 1, [&](int u) { t^= u; }); --s&= t;) g[s]*= x;
  return sps::exp(g)[N - 1] * pow(y, j);
 }
 template <class T> inline T perfect_matching() const { return sps::exp(cyc<T>()).back(); }
 template <class T> inline T all_matching() const {
  auto [cyc, pth]= cyc_pth<T>();
  for (int s= cyc.size(); s--;) cyc[s]+= pth[s];
  return sps::exp(cyc).back();
 }
 template <class T> std::vector<T> k_mathcing() const {
  auto [cyc, pth]= cyc_pth<T>();
  auto ret= sps::egf_T(pth, sps::exp(cyc));
  return std::reverse(ret.begin(), ret.end()), ret.resize(n / 2 + 1), ret;
 }
};
#line 6 "test/yukicoder/2507.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int n, m;
 cin >> n >> m;
 UndirectedGraphSetPowerSeries g(n);
 for (int i= 0, u, v; i < m; ++i) cin >> u >> v, g.add_edge(--u, --v);
 auto f= g.cycle_graph<long long>();
 for (int i= n; i--;) f[1 << i]= 1;
 cout << g.disjoint_union(g.bridge_union(f)).back() << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	00_example_00.in	AC	6 ms	4 MB
g++-13	00_example_01.in	AC	5 ms	4 MB
g++-13	01_random_small_00.in	AC	5 ms	4 MB
g++-13	01_random_small_01.in	AC	5 ms	4 MB
g++-13	01_random_small_02.in	AC	5 ms	4 MB
g++-13	01_random_small_03.in	AC	5 ms	4 MB
g++-13	01_random_small_04.in	AC	5 ms	4 MB
g++-13	01_random_small_05.in	AC	5 ms	4 MB
g++-13	01_random_small_06.in	AC	5 ms	4 MB
g++-13	01_random_small_07.in	AC	5 ms	4 MB
g++-13	01_random_small_08.in	AC	5 ms	4 MB
g++-13	01_random_small_09.in	AC	5 ms	4 MB
g++-13	01_random_small_10.in	AC	5 ms	4 MB
g++-13	01_random_small_11.in	AC	5 ms	4 MB
g++-13	01_random_small_12.in	AC	5 ms	4 MB
g++-13	01_random_small_13.in	AC	5 ms	4 MB
g++-13	01_random_small_14.in	AC	5 ms	4 MB
g++-13	01_random_small_15.in	AC	5 ms	4 MB
g++-13	01_random_small_16.in	AC	5 ms	4 MB
g++-13	01_random_small_17.in	AC	5 ms	4 MB
g++-13	01_random_small_18.in	AC	5 ms	4 MB
g++-13	01_random_small_19.in	AC	5 ms	4 MB
g++-13	02_random_00.in	AC	5 ms	4 MB
g++-13	02_random_01.in	AC	5 ms	4 MB
g++-13	02_random_02.in	AC	5 ms	4 MB
g++-13	02_random_03.in	AC	6 ms	4 MB
g++-13	02_random_04.in	AC	10 ms	4 MB
g++-13	02_random_05.in	AC	5 ms	4 MB
g++-13	02_random_06.in	AC	6 ms	4 MB
g++-13	02_random_07.in	AC	5 ms	4 MB
g++-13	02_random_08.in	AC	10 ms	4 MB
g++-13	03_random_sparse_00.in	AC	18 ms	5 MB
g++-13	03_random_sparse_01.in	AC	18 ms	5 MB
g++-13	03_random_sparse_02.in	AC	6 ms	4 MB
g++-13	04_random_disconnected_00.in	AC	6 ms	4 MB
g++-13	04_random_disconnected_01.in	AC	6 ms	4 MB
g++-13	04_random_disconnected_02.in	AC	5 ms	4 MB
g++-13	05_random_max_00.in	AC	18 ms	5 MB
g++-13	05_random_max_01.in	AC	19 ms	5 MB
g++-13	05_random_max_02.in	AC	19 ms	5 MB
g++-13	05_random_max_03.in	AC	19 ms	5 MB
g++-13	05_random_max_04.in	AC	19 ms	5 MB
g++-13	06_max_clique_00.in	AC	19 ms	5 MB
g++-13	07_cycles_00.in	AC	11 ms	4 MB
g++-13	07_cycles_01.in	AC	18 ms	5 MB
g++-13	07_cycles_02.in	AC	6 ms	4 MB
g++-13	08_tree_00.in	AC	6 ms	4 MB
g++-13	08_tree_01.in	AC	18 ms	5 MB
g++-13	09_cliques_00.in	AC	6 ms	4 MB
g++-13	09_cliques_01.in	AC	19 ms	5 MB
g++-13	10_grid_00.in	AC	6 ms	4 MB
g++-13	10_grid_01.in	AC	10 ms	4 MB
clang++-18	00_example_00.in	AC	6 ms	4 MB
clang++-18	00_example_01.in	AC	5 ms	4 MB
clang++-18	01_random_small_00.in	AC	5 ms	4 MB
clang++-18	01_random_small_01.in	AC	5 ms	4 MB
clang++-18	01_random_small_02.in	AC	5 ms	4 MB
clang++-18	01_random_small_03.in	AC	5 ms	4 MB
clang++-18	01_random_small_04.in	AC	5 ms	4 MB
clang++-18	01_random_small_05.in	AC	5 ms	4 MB
clang++-18	01_random_small_06.in	AC	5 ms	4 MB
clang++-18	01_random_small_07.in	AC	5 ms	4 MB
clang++-18	01_random_small_08.in	AC	5 ms	4 MB
clang++-18	01_random_small_09.in	AC	5 ms	4 MB
clang++-18	01_random_small_10.in	AC	5 ms	4 MB
clang++-18	01_random_small_11.in	AC	5 ms	4 MB
clang++-18	01_random_small_12.in	AC	6 ms	4 MB
clang++-18	01_random_small_13.in	AC	5 ms	4 MB
clang++-18	01_random_small_14.in	AC	5 ms	4 MB
clang++-18	01_random_small_15.in	AC	5 ms	4 MB
clang++-18	01_random_small_16.in	AC	5 ms	4 MB
clang++-18	01_random_small_17.in	AC	5 ms	4 MB
clang++-18	01_random_small_18.in	AC	5 ms	4 MB
clang++-18	01_random_small_19.in	AC	5 ms	4 MB
clang++-18	02_random_00.in	AC	5 ms	4 MB
clang++-18	02_random_01.in	AC	5 ms	4 MB
clang++-18	02_random_02.in	AC	5 ms	4 MB
clang++-18	02_random_03.in	AC	6 ms	4 MB
clang++-18	02_random_04.in	AC	10 ms	4 MB
clang++-18	02_random_05.in	AC	6 ms	4 MB
clang++-18	02_random_06.in	AC	6 ms	4 MB
clang++-18	02_random_07.in	AC	5 ms	4 MB
clang++-18	02_random_08.in	AC	10 ms	4 MB
clang++-18	03_random_sparse_00.in	AC	19 ms	5 MB
clang++-18	03_random_sparse_01.in	AC	20 ms	5 MB
clang++-18	03_random_sparse_02.in	AC	7 ms	4 MB
clang++-18	04_random_disconnected_00.in	AC	6 ms	4 MB
clang++-18	04_random_disconnected_01.in	AC	6 ms	4 MB
clang++-18	04_random_disconnected_02.in	AC	5 ms	4 MB
clang++-18	05_random_max_00.in	AC	19 ms	5 MB
clang++-18	05_random_max_01.in	AC	20 ms	5 MB
clang++-18	05_random_max_02.in	AC	20 ms	5 MB
clang++-18	05_random_max_03.in	AC	20 ms	5 MB
clang++-18	05_random_max_04.in	AC	20 ms	5 MB
clang++-18	06_max_clique_00.in	AC	20 ms	5 MB
clang++-18	07_cycles_00.in	AC	12 ms	4 MB
clang++-18	07_cycles_01.in	AC	20 ms	5 MB
clang++-18	07_cycles_02.in	AC	7 ms	4 MB
clang++-18	08_tree_00.in	AC	6 ms	4 MB
clang++-18	08_tree_01.in	AC	20 ms	5 MB
clang++-18	09_cliques_00.in	AC	6 ms	4 MB
clang++-18	09_cliques_01.in	AC	20 ms	5 MB
clang++-18	10_grid_00.in	AC	6 ms	4 MB
clang++-18	10_grid_01.in	AC	11 ms	4 MB

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