結果

問題 No.1421 国勢調査 (Hard)
ユーザー hashiryohashiryo
提出日時 2024-09-03 10:53:28
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 256 ms / 2,000 ms
コード長 23,626 bytes
コンパイル時間 2,772 ms
コンパイル使用メモリ 220,452 KB
実行使用メモリ 11,508 KB
最終ジャッジ日時 2024-09-03 10:53:36
合計ジャッジ時間 7,658 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
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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 3 ms
6,816 KB
testcase_01 AC 3 ms
6,940 KB
testcase_02 AC 3 ms
6,940 KB
testcase_03 AC 3 ms
6,944 KB
testcase_04 AC 3 ms
6,940 KB
testcase_05 AC 3 ms
6,940 KB
testcase_06 AC 3 ms
6,940 KB
testcase_07 AC 4 ms
6,940 KB
testcase_08 AC 4 ms
6,944 KB
testcase_09 AC 3 ms
6,944 KB
testcase_10 AC 4 ms
6,944 KB
testcase_11 AC 3 ms
6,944 KB
testcase_12 AC 3 ms
6,944 KB
testcase_13 AC 6 ms
6,940 KB
testcase_14 AC 3 ms
6,940 KB
testcase_15 AC 3 ms
6,944 KB
testcase_16 AC 3 ms
6,940 KB
testcase_17 AC 3 ms
6,940 KB
testcase_18 AC 3 ms
6,944 KB
testcase_19 AC 3 ms
6,944 KB
testcase_20 AC 3 ms
6,940 KB
testcase_21 AC 3 ms
6,944 KB
testcase_22 AC 227 ms
11,504 KB
testcase_23 AC 233 ms
11,372 KB
testcase_24 AC 229 ms
11,364 KB
testcase_25 AC 252 ms
11,392 KB
testcase_26 AC 231 ms
11,432 KB
testcase_27 AC 231 ms
11,368 KB
testcase_28 AC 228 ms
11,508 KB
testcase_29 AC 230 ms
11,360 KB
testcase_30 AC 256 ms
11,440 KB
testcase_31 AC 232 ms
11,392 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
// clang-format off
std::ostream&operator<<(std::ostream&os,std::int8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,std::uint8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,const __int128_t &u){if(!u)os<<"0";__int128_t tmp=u<0?(os<<"-",-u):u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
std::ostream&operator<<(std::ostream&os,const __uint128_t &u){if(!u)os<<"0";__uint128_t tmp=u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
#define checkpoint() (void(0))
#define debug(...) (void(0))
#define debugArray(x,n) (void(0))
#define debugMatrix(x,h,w) (void(0))
// clang-format on
#include <type_traits>
namespace _la_internal {
using namespace std;
template <class R> struct Vector {
 valarray<R> dat;
 Vector()= default;
 Vector(size_t n): dat(n) {}
 Vector(size_t n, const R &v): dat(v, n) {}
 Vector(const initializer_list<R> &v): dat(v) {}
 R &operator[](int i) { return dat[i]; }
 const R &operator[](int i) const { return dat[i]; }
 bool operator==(const Vector &r) const {
  if (dat.size() != r.dat.size()) return false;
  for (int i= dat.size(); i--;)
   if (dat[i] != r.dat[i]) return false;
  return true;
 }
 bool operator!=(const Vector &r) const { return !(*this == r); }
 explicit operator bool() const { return dat.size(); }
 Vector operator-() const { return Vector(dat.size())-= *this; }
 Vector &operator+=(const Vector &r) { return dat+= r.dat, *this; }
 Vector &operator-=(const Vector &r) { return dat-= r.dat, *this; }
 Vector &operator*=(const R &r) { return dat*= r, *this; }
 Vector operator+(const Vector &r) const { return Vector(*this)+= r; }
 Vector operator-(const Vector &r) const { return Vector(*this)-= r; }
 Vector operator*(const R &r) const { return Vector(*this)*= r; }
 size_t size() const { return dat.size(); }
 friend R dot(const Vector<R> &a, const Vector<R> &b) { return assert(a.size() == b.size()), (a.dat * b.dat).sum(); }
};
using u128= __uint128_t;
using u64= uint64_t;
using u8= uint8_t;
class Ref {
 u128 *ref;
 u8 i;
public:
 Ref(u128 *ref, u8 i): ref(ref), i(i) {}
 Ref &operator=(const Ref &r) { return *this= bool(r); }
 Ref &operator=(bool b) { return *ref&= ~(u128(1) << i), *ref|= u128(b) << i, *this; }
 Ref &operator|=(bool b) { return *ref|= u128(b) << i, *this; }
 Ref &operator&=(bool b) { return *ref&= ~(u128(!b) << i), *this; }
 Ref &operator^=(bool b) { return *ref^= u128(b) << i, *this; }
 operator bool() const { return (*ref >> i) & 1; }
};
template <> class Vector<bool> {
 size_t n;
public:
 valarray<u128> dat;
 Vector(): n(0) {}
 Vector(size_t n): n(n), dat((n + 127) >> 7) {}
 Vector(size_t n, bool b): n(n), dat(-u128(b), (n + 127) >> 7) {
  if (int k= n & 127; k) dat[dat.size() - 1]&= (u128(1) << k) - 1;
 }
 Vector(const initializer_list<bool> &v): n(v.size()), dat((n + 127) >> 7) {
  int i= 0;
  for (bool b: v) dat[i >> 7]|= u128(b) << (i & 127), ++i;
 }
 Ref operator[](int i) { return {begin(dat) + (i >> 7), u8(i & 127)}; }
 bool operator[](int i) const { return (dat[i >> 7] >> (i & 127)) & 1; }
 bool operator==(const Vector &r) const {
  if (dat.size() != r.dat.size()) return false;
  for (int i= dat.size(); i--;)
   if (dat[i] != r.dat[i]) return false;
  return true;
 }
 bool operator!=(const Vector &r) const { return !(*this == r); }
 explicit operator bool() const { return n; }
 Vector operator-() const { return Vector(*this); }
 Vector &operator+=(const Vector &r) { return dat^= r.dat, *this; }
 Vector &operator-=(const Vector &r) { return dat^= r.dat, *this; }
 Vector &operator*=(bool b) { return dat*= b, *this; }
 Vector operator+(const Vector &r) const { return Vector(*this)+= r; }
 Vector operator-(const Vector &r) const { return Vector(*this)-= r; }
 Vector operator*(bool b) const { return Vector(*this)*= b; }
 size_t size() const { return n; }
 friend bool dot(const Vector<bool> &a, const Vector<bool> &b) {
  assert(a.size() == b.size());
  u128 v= 0;
  for (int i= a.dat.size(); i--;) v^= a.dat[i] & b.dat[i];
  return __builtin_parityll(v >> 64) ^ __builtin_parityll(u64(v));
 }
};
template <class R> Vector<R> operator*(const R &r, const Vector<R> &v) { return v * r; }
template <class R> ostream &operator<<(ostream &os, const Vector<R> &v) {
 os << '[';
 for (int _= 0, __= v.size(); _ < __; ++_) os << (_ ? ", " : "") << v[_];
 return os << ']';
}
}
using _la_internal::Vector;
namespace _la_internal {
template <class R, class D> struct Mat {
 Mat(): W(0) {}
 Mat(size_t h, size_t w): W(w), dat(h * w) {}
 Mat(size_t h, size_t w, R v): W(w), dat(v, h * w) {}
 Mat(initializer_list<initializer_list<R>> v): W(v.size() ? v.begin()->size() : 0), dat(v.size() * W) {
  auto it= begin(dat);
  for (const auto &r: v) {
   assert(r.size() == W);
   for (R x: r) *it++= x;
  }
 }
 size_t width() const { return W; }
 size_t height() const { return W ? dat.size() / W : 0; }
 auto operator[](int i) { return next(begin(dat), i * W); }
 auto operator[](int i) const { return next(begin(dat), i * W); }
protected:
 size_t W;
 valarray<R> dat;
 void add(const Mat &r) { assert(dat.size() == r.dat.size()), assert(W == r.W), dat+= r.dat; }
 D mul(const Mat &r) const {
  const size_t h= height(), w= r.W, l= W;
  assert(l == r.height());
  D ret(h, w);
  auto a= begin(dat);
  auto c= begin(ret.dat);
  for (int i= h; i--; advance(c, w)) {
   auto b= begin(r.dat);
   for (int k= l; k--; ++a) {
    auto d= c;
    auto v= *a;
    for (int j= w; j--; ++b, ++d) *d+= v * *b;
   }
  }
  return ret;
 }
 Vector<R> mul(const Vector<R> &r) const {
  assert(W == r.size());
  const size_t h= height();
  Vector<R> ret(h);
  auto a= begin(dat);
  for (size_t i= 0; i < h; ++i)
   for (size_t k= 0; k < W; ++k, ++a) ret[i]+= *a * r[k];
  return ret;
 }
};
template <class D> struct Mat<bool, D> {
 struct Array {
  u128 *bg;
  Array(u128 *it): bg(it) {}
  Ref operator[](int i) { return Ref{bg + (i >> 7), u8(i & 127)}; }
  bool operator[](int i) const { return (bg[i >> 7] >> (i & 127)) & 1; }
 };
 struct ConstArray {
  const u128 *bg;
  ConstArray(const u128 *it): bg(it) {}
  bool operator[](int i) const { return (bg[i >> 7] >> (i & 127)) & 1; }
 };
 Mat(): H(0), W(0), m(0) {}
 Mat(size_t h, size_t w): H(h), W(w), m((w + 127) >> 7), dat(h * m) {}
 Mat(size_t h, size_t w, bool b): H(h), W(w), m((w + 127) >> 7), dat(-u128(b), h * m) {
  if (size_t i= h, k= w & 127; k)
   for (u128 s= (u128(1) << k) - 1; i--;) dat[i * m]&= s;
 }
 Mat(const initializer_list<initializer_list<bool>> &v): H(v.size()), W(H ? v.begin()->size() : 0), m((W + 127) >> 7), dat(H * m) {
  auto it= begin(dat);
  for (const auto &r: v) {
   assert(r.size() == W);
   int i= 0;
   for (bool b: r) it[i >> 7]|= u128(b) << (i & 127), ++i;
   advance(it, m);
  }
 }
 size_t width() const { return W; }
 size_t height() const { return H; }
 Array operator[](int i) { return {next(begin(dat), i * m)}; }
 ConstArray operator[](int i) const { return {next(begin(dat), i * m)}; }
 ConstArray get(int i) const { return {next(begin(dat), i * m)}; }
protected:
 size_t H, W, m;
 valarray<u128> dat;
 void add(const Mat &r) { assert(H == r.H), assert(W == r.W), dat^= r.dat; }
 D mul(const Mat &r) const {
  assert(W == r.H);
  D ret(H, r.W);
  u128 *c= begin(ret.dat);
  for (size_t i= 0; i < H; ++i, advance(c, r.m)) {
   ConstArray a= this->operator[](i);
   const u128 *b= begin(r.dat);
   for (size_t k= 0; k < W; ++k, advance(b, r.m))
    if (a[k])
     for (size_t j= 0; j < r.m; ++j) c[j]^= b[j];
  }
  return ret;
 }
 Vector<bool> mul(const Vector<bool> &r) const {
  assert(W == r.size());
  Vector<bool> ret(H);
  auto a= begin(dat);
  for (size_t i= 0; i < H; ++i) {
   u128 v= 0;
   for (size_t j= 0; j < m; ++j, ++a) v^= *a & r.dat[j];
   ret[i]= __builtin_parityll(v >> 64) ^ __builtin_parityll(u64(v));
  }
  return ret;
 }
};
template <class R> struct Matrix: public Mat<R, Matrix<R>> {
 using Mat<R, Matrix<R>>::Mat;
 explicit operator bool() const { return this->W; }
 static Matrix identity_matrix(int n) {
  Matrix ret(n, n);
  for (; n--;) ret[n][n]= R(true);
  return ret;
 }
 Matrix submatrix(const vector<int> &rows, const vector<int> &cols) const {
  Matrix ret(rows.size(), cols.size());
  for (int i= rows.size(); i--;)
   for (int j= cols.size(); j--;) ret[i][j]= (*this)[rows[i]][cols[j]];
  return ret;
 }
 Matrix submatrix_rm(vector<int> rows, vector<int> cols) const {
  sort(begin(rows), end(rows)), sort(begin(cols), end(cols)), rows.erase(unique(begin(rows), end(rows)), end(rows)), cols.erase(unique(begin(cols), end(cols)), end(cols));
  const int H= this->height(), W= this->width(), n= rows.size(), m= cols.size();
  vector<int> rs(H - n), cs(W - m);
  for (int i= 0, j= 0, k= 0; i < H; ++i)
   if (j < n && rows[j] == i) ++j;
   else rs[k++]= i;
  for (int i= 0, j= 0, k= 0; i < W; ++i)
   if (j < m && cols[j] == i) ++j;
   else cs[k++]= i;
  return submatrix(rs, cs);
 }
 bool operator==(const Matrix &r) const {
  if (this->width() != r.width() || this->height() != r.height()) return false;
  for (int i= this->dat.size(); i--;)
   if (this->dat[i] != r.dat[i]) return false;
  return true;
 }
 bool operator!=(const Matrix &r) const { return !(*this == r); }
 Matrix &operator*=(const Matrix &r) { return *this= this->mul(r); }
 Matrix operator*(const Matrix &r) const { return this->mul(r); }
 Matrix &operator*=(R r) { return this->dat*= r, *this; }
 template <class T> Matrix operator*(T r) const {
  static_assert(is_convertible_v<T, R>);
  return Matrix(*this)*= r;
 }
 Matrix &operator+=(const Matrix &r) { return this->add(r), *this; }
 Matrix operator+(const Matrix &r) const { return Matrix(*this)+= r; }
 Vector<R> operator*(const Vector<R> &r) const { return this->mul(r); }
 Vector<R> operator()(const Vector<R> &r) const { return this->mul(r); }
 Matrix pow(uint64_t k) const {
  size_t W= this->width();
  assert(W == this->height());
  for (Matrix ret= identity_matrix(W), b= *this;; b*= b)
   if (k & 1 ? ret*= b, !(k>>= 1) : !(k>>= 1)) return ret;
 }
};
template <class R, class T> Matrix<R> operator*(const T &r, const Matrix<R> &m) { return m * r; }
template <class R> ostream &operator<<(ostream &os, const Matrix<R> &m) {
 os << "\n[";
 for (int i= 0, h= m.height(); i < h; os << ']', ++i) {
  if (i) os << "\n ";
  os << '[';
  for (int j= 0, w= m.width(); j < w; ++j) os << (j ? ", " : "") << m[i][j];
 }
 return os << ']';
}
template <class K> static bool is_zero(K x) {
 if constexpr (is_floating_point_v<K>) return abs(x) < 1e-8;
 else return x == K();
}
}
using _la_internal::Matrix;
namespace _la_internal {
template <class K> class LU_Decomposition {
 Matrix<K> dat;
 vector<size_t> perm, piv;
 bool sgn;
 size_t psz;
public:
 LU_Decomposition(const Matrix<K> &A): dat(A), perm(A.height()), sgn(false), psz(0) {
  const size_t h= A.height(), w= A.width();
  iota(perm.begin(), perm.end(), 0), piv.resize(min(w, h));
  for (size_t c= 0, pos; c < w && psz < h; ++c) {
   pos= psz;
   if constexpr (is_floating_point_v<K>) {
    for (size_t r= psz + 1; r < h; ++r)
     if (abs(dat[perm[pos]][c]) < abs(dat[perm[r]][c])) pos= r;
   } else if (is_zero(dat[perm[pos]][c]))
    for (size_t r= psz + 1; r < h; ++r)
     if (!is_zero(dat[perm[r]][c])) pos= r, r= h;
   if (is_zero(dat[perm[pos]][c])) continue;
   if (pos != psz) sgn= !sgn, swap(perm[pos], perm[psz]);
   const auto b= dat[perm[psz]];
   for (size_t r= psz + 1, i; r < h; ++r) {
    auto a= dat[perm[r]];
    K m= a[c] / b[c];
    for (a[c]= K(), a[psz]= m, i= c + 1; i < w; ++i) a[i]-= b[i] * m;
   }
   piv[psz++]= c;
  }
 }
 size_t rank() const { return psz; }
 bool is_regular() const { return rank() == dat.height() && rank() == dat.width(); }
 K det() const {
  assert(dat.height() == dat.width());
  K ret= sgn ? -1 : 1;
  for (size_t i= dat.width(); i--;) ret*= dat[perm[i]][i];
  return ret;
 }
 vector<Vector<K>> kernel() const {
  const size_t w= dat.width(), n= rank();
  vector ker(w - n, Vector<K>(w));
  for (size_t c= 0, i= 0; c < w; ++c) {
   if (i < n && piv[i] == c) ++i;
   else {
    auto &a= ker[c - i];
    a[c]= 1;
    for (size_t r= i; r--;) a[r]= -dat[perm[r]][c];
    for (size_t j= i, k, r; j--;) {
     K x= a[j] / dat[perm[j]][k= piv[j]];
     for (a[j]= 0, a[k]= x, r= j; r--;) a[r]-= dat[perm[r]][k] * x;
    }
   }
  }
  return ker;
 }
 Vector<K> linear_equations(const Vector<K> &b) const {
  const size_t h= dat.height(), w= dat.width(), n= rank();
  assert(h == b.size());
  Vector<K> y(h), x(w);
  for (size_t c= 0; c < h; ++c)
   if (y[c]+= b[perm[c]]; c < w)
    for (size_t r= c + 1; r < h; ++r) y[r]-= y[c] * dat[perm[r]][c];
  for (size_t i= n; i < h; ++i)
   if (!is_zero(y[i])) return Vector<K>();  // no solution
  for (size_t i= n, r; i--;)
   for (x[piv[i]]= y[i] / dat[perm[i]][piv[i]], r= i; r--;) y[r]-= x[piv[i]] * dat[perm[r]][piv[i]];
  return x;
 }
 Matrix<K> inverse_matrix() const {
  if (!is_regular()) return Matrix<K>();  // no solution
  const size_t n= dat.width();
  Matrix<K> ret(n, n);
  for (size_t i= 0; i < n; ++i) {
   Vector<K> y(n);
   for (size_t c= 0; c < n; ++c)
    if (y[c]+= perm[c] == i; c < n && !is_zero(y[c]))
     for (size_t r= c + 1; r < n; ++r) y[r]-= y[c] * dat[perm[r]][c];
   for (size_t j= n; j--;) {
    K m= ret[j][i]= y[j] / dat[perm[j]][j];
    for (size_t r= j; r--;) y[r]-= m * dat[perm[r]][j];
   }
  }
  return ret;
 }
};
void add_upper(u128 *a, const u128 *b, size_t bg, size_t ed) {  //[bg,ed)
 if (bg >= ed) return;
 size_t s= bg >> 7;
 a[s]^= b[s] & -(u128(1) << (bg & 127));
 for (size_t i= (ed + 127) >> 7; --i > s;) a[i]^= b[i];
}
void add_lower(u128 *a, const u128 *b, size_t ed) {  //[0,ed)
 size_t s= ed >> 7;
 a[s]^= b[s] & ((u128(1) << (ed & 127)) - 1);
 for (size_t i= s; i--;) a[i]^= b[i];
}
void subst_lower(u128 *a, const u128 *b, size_t ed) {  //[0,ed)
 size_t s= ed >> 7;
 a[s]= b[s] & ((u128(1) << (ed & 127)) - 1);
 for (size_t i= s; i--;) a[i]= b[i];
}
bool any1_upper(const u128 *a, size_t bg, size_t ed) {  //[bg,ed)
 if (bg >= ed) return false;
 size_t s= bg >> 7;
 if (a[s] & -(u128(1) << (bg & 127))) return true;
 for (size_t i= (ed + 127) >> 7; --i > s;)
  if (a[i]) return true;
 return false;
}
template <> class LU_Decomposition<bool> {
 Matrix<bool> dat;
 vector<size_t> perm, piv;
 size_t psz;
public:
 LU_Decomposition(Matrix<bool> A): dat(A.width(), A.height()), perm(A.height()), psz(0) {
  const size_t h= A.height(), w= A.width();
  iota(perm.begin(), perm.end(), 0), piv.resize(min(w, h));
  for (size_t c= 0, pos; c < w && psz < h; ++c) {
   for (pos= psz; pos < h; ++pos)
    if (A.get(perm[pos])[c]) break;
   if (pos == h) continue;
   if (pos != psz) swap(perm[pos], perm[psz]);
   auto b= A.get(perm[psz]);
   for (size_t r= psz + 1; r < h; ++r) {
    auto a= A[perm[r]];
    if (bool m= a[c]; m) add_upper(a.bg, b.bg, c, w), a[psz]= 1;
   }
   piv[psz++]= c;
  }
  for (size_t j= w; j--;)
   for (size_t i= h; i--;) dat[j][i]= A.get(perm[i])[j];
 }
 size_t rank() const { return psz; }
 bool is_regular() const { return rank() == dat.height() && rank() == dat.width(); }
 bool det() const { return is_regular(); }
 vector<Vector<bool>> kernel() const {
  const size_t w= dat.height(), n= rank();
  vector ker(w - rank(), Vector<bool>(w));
  for (size_t c= 0, i= 0; c < w; ++c) {
   if (i < n && piv[i] == c) ++i;
   else {
    auto &a= ker[c - i];
    subst_lower(begin(a.dat), dat[c].bg, i), a[c]= 1;
    for (size_t j= i, k; j--;) {
     bool x= a[j];
     if (a[j]= 0, a[k= piv[j]]= x; x) add_lower(begin(a.dat), dat[k].bg, j);
    }
   }
  }
  return ker;
 }
 Vector<bool> linear_equations(const Vector<bool> &b) const {
  const size_t h= dat.width(), w= dat.height(), n= rank();
  assert(h == b.size());
  Vector<bool> y(h), x(w);
  for (size_t c= 0; c < h; ++c)
   if (y[c]^= b[perm[c]]; c < w && y[c]) add_upper(begin(y.dat), dat[c].bg, c + 1, h);
  if (any1_upper(begin(y.dat), n, h)) return Vector<bool>();  // no solution
  for (size_t i= n; i--;)
   if ((x[piv[i]]= y[i])) add_lower(begin(y.dat), dat[piv[i]].bg, i);
  return x;
 }
 Matrix<bool> inverse_matrix() const {
  if (!is_regular()) return Matrix<bool>();  // no solution
  const size_t n= dat.width();
  Matrix<bool> ret(n, n);
  for (size_t i= 0; i < n; ++i) {
   Vector<bool> y(n);
   for (size_t c= 0; c < n; ++c)
    if (y[c]^= perm[c] == i; c < n && y[c]) add_upper(begin(y.dat), dat[c].bg, c, n);
   for (size_t j= n; j--;)
    if ((ret[j][i]= y[j])) add_lower(begin(y.dat), dat[j].bg, j);
  }
  return ret;
 }
};
}
using _la_internal::LU_Decomposition;
class Nimber {
 using u64= unsigned long long;
 using u32= unsigned;
 using u16= unsigned short;
 static inline std::array<u16, 65536> pw, ln;
 template <u16 h= 3> static inline u16 half(u16 A) { return A ? pw[(ln[A] + h) % 65535] : 0; }
 template <u16 h= 0> static inline u16 mul(u16 A, u16 B) { return A && B ? pw[(ln[A] + ln[B] + h) % 65535] : 0; }
 template <u16 h= 0> static inline u16 mul(u16 A, u16 B, u16 C) { return A && B && C ? pw[(ln[A] + ln[B] + ln[C] + h) % 65535] : 0; }
 static inline u16 inv(u16 A) { return assert(A), pw[65535 - ln[A]]; }
 static inline u16 sqrt(u16 A) { return A ? pw[u16((65537 * u32(ln[A])) >> 1)] : 0; }
 static inline u64 mul(u64 A, u64 B) {
  u16 a0= u16(A), a1= u16(A >> 16), a2= u16(A >> 32), a3= A >> 48, b0= u16(B), b1= u16(B >> 16), b2= u16(B >> 32), b3= B >> 48, x0= a1 ^ a0, x1= a3 ^ a2, y0= b1 ^ b0, y1= b3 ^ b2, c0= mul(a0, b0), c1= mul(x0, y0) ^ c0, c2= mul<0>(a2 ^ a0, b2 ^ b0), c3= mul<0>(x0 ^ x1, y0 ^ y1) ^ c2 ^ c1;
  return c2^= (c0^= mul<3>(a1, b1)) ^ mul<3>(u16(a3 ^ a1), u16(b3 ^ b1)), c1^= mul<6>(a3, b3) ^ mul<3>(x1, y1), c0^= mul<6>(a2, b2) ^ mul<6>(x1, y1), (u64(c3) << 48) | (u64(c2) << 32) | (u32(c1) << 16) | c0;
 }
 static inline u64 inv(u64 A) {
  u16 a0= u16(A), a1= u16(A >> 16), a2= u16(A >> 32), a3= A >> 48, x= a2 ^ a3, y= a1 ^ a3, w= a0 ^ a2, v= a0 ^ a1, b3= mul(a1, a2, a1 ^ x), b2= mul(a0, a2, a0 ^ x), b1= mul(a0, a1, a0 ^ y), b0= mul(a0, v, w), t= mul<3>(w, x, x);
  return b0^= b1 ^ b2, b1^= b3, b2^= b3, b0^= b3^= mul(a0, a0, a3), b1^= t ^ mul<3>(a1, y, y), b0^= t ^ mul<3>(v, y, y), b3^= t= mul<3>(a1, a3, y) ^ mul<3>(a2, x, x), b2^= t ^ mul<3>(a0, a3, a3) ^ mul<3>(a1, a1, a2), b3^= mul<6>(a3, a3, x), b2^= mul<6>(a3, x, x), b1^= mul<6>(a3, a3, y ^ w), b0^= mul<6>(y, x, x), b2^= mul<9>(a3, a3, a3), b0^= mul<9>(a3, a3, y), t= mul<6>(x, b3) ^ mul<6>(a3, b2) ^ mul<3>(a1, b1) ^ mul(a0, b0), t= inv(t), (u64(mul(b3, t)) << 48) | (u64(mul(b2, t)) << 32) | (u32(mul(b1, t)) << 16) | mul(b0, t);
 }
 static inline u64 square(u64 A) {
  u16 a0= u16(A), a1= u16(A >> 16), a2= u16(A >> 32), a3= A >> 48;
  return a3= mul(a3, a3), a2= mul(a2, a2), a1= mul(a1, a1), a0= mul(a0, a0), a0^= half(a1) ^ half<6>(a3), a2^= half(a3), a1^= half(a3 ^ a2), (u64(a3) << 48) | (u64(a2) << 32) | (u32(a1) << 16) | a0;
 }
 static inline u64 pow(u64 A, u64 k) {
  for (u64 ret= 1;; A= square(A))
   if (k & 1 ? ret= mul(ret, A) : 0; !(k>>= 1)) return ret;
 }
 template <int mod> static inline int mdif(int a, int b) { return a+= mod & -((a-= b) < 0); }
 template <int mod> static inline int mmul(int a, int b) { return u64(a) * b % mod; }
 static inline int log16(u16 A, u16 B) {
  int a= ln[A], b= ln[B], x= 1;
  if (a == 0) return b == 0 ? 1 : -1;
  for (int q, z, u, y= 0, t= 65535; t;) z= x, u= a, x= y, y= z - y * (q= a / t), a= t, t= u - t * q;
  return b % a ? -1 : u32(b / a) * (x < 0 ? 65535 + x : x) % 65535;
 }
 template <int period, int size> static inline int bsgs(u64 x, u64 y) {
  static constexpr int mask= size - 1;
  std::pair<u64, int> vs[size];
  int os[size + 1]= {};
  u64 so[size], big= 1;
  for (int i= 0; i < size; ++i, big= mul(big, x)) ++os[(so[i]= big) & mask];
  for (int i= 0; i < size; ++i) os[i + 1]+= os[i];
  for (int i= 0; i < size; ++i) vs[--os[so[i] & mask]]= {so[i], i};
  for (int t= 0; t < period; t+= size, y= mul(y, big))
   for (int m= (y & mask), i= os[m], ret; i < os[m + 1]; ++i)
    if (y == vs[i].first) return (ret= vs[i].second - t) < 0 ? ret + period : ret;
  return -1;
 }
 static inline u64 log(u64 A, u64 B) {
  if (B == 1) return 0;
  if (!A && !B) return 1;
  if (!A || !B) return u64(-1);
  static constexpr int P0= 641, P1= 65535, P2= 65537, P3= 6700417, iv10= 40691, iv21= 32768, iv20= 45242, iv32= 3317441, iv31= 3350208, iv30= 3883315;
  int a0= bsgs<P0, 16>(pow(A, 0x663d80ff99c27f), pow(B, 0x663d80ff99c27f));
  if (a0 == -1) return u64(-1);
  int a1= log16(pow(A, 0x1000100010001), pow(B, 0x1000100010001));
  if (a1 == -1) return u64(-1);
  int a2= bsgs<P2, 256>(pow(A, 0xffff0000ffff), pow(B, 0xffff0000ffff));
  if (a2 == -1) return u64(-1);
  int a3= bsgs<P3, 2048>(pow(A, 0x280fffffd7f), pow(B, 0x280fffffd7f));
  if (a3 == -1) return u64(-1);
  int x1= mmul<P1>(mdif<P1>(a1, a0), iv10), x2= mdif<P2>(mmul<P2>(mdif<P2>(a2, a0), iv20), mmul<P2>(x1, iv21)), x3= mdif<P3>(mdif<P3>(mmul<P3>(mdif<P3>(a3, a0), iv30), mmul<P3>(x1, iv31)), mmul<P3>(x2, iv32));
  return u64(P0) * (u64(P1) * (u64(P2) * x3 + x2) + x1) + a0;
 }
 u64 x;
public:
 static inline void init(u32 x= 0, u32 y= 0) {
  constexpr u16 f2n[16]= {0x0001u, 0x2827u, 0x392bu, 0x8000u, 0x20fdu, 0x4d1du, 0xde4au, 0x0a17u, 0x3464u, 0xe3a9u, 0x6d8du, 0x34bcu, 0xa921u, 0xa173u, 0x0ebcu, 0x0e69u};
  for (int i= pw[0]= pw[65535]= 1; i < 65535; ++i) pw[i]= (pw[i - 1] << 1) ^ (0x1681fu & (-(pw[i - 1] >= 0x8000u)));
  for (int i= 1; i < 65535; ln[pw[i]= y]= i, i++)
   for (x= pw[i], y= 0; x; x&= x - 1) y^= f2n[__builtin_ctz(x)];
 }
 Nimber(u64 x_= 0): x(x_) {}
 Nimber &operator+=(const Nimber &r) { return x^= r.x, *this; }
 Nimber &operator-=(const Nimber &r) { return x^= r.x, *this; }
 Nimber &operator*=(const Nimber &r) { return x= mul(x, r.x), *this; }
 Nimber &operator/=(const Nimber &r) { return x= mul(x, inv(r.x)), *this; }
 Nimber operator+(const Nimber &r) const { return Nimber(x ^ r.x); }
 Nimber operator-(const Nimber &r) const { return Nimber(x ^ r.x); }
 Nimber operator*(const Nimber &r) const { return Nimber(mul(x, r.x)); }
 Nimber operator/(const Nimber &r) const { return Nimber(mul(x, inv(r.x))); }
 Nimber operator-() const { return *this; }
 Nimber inv() const { return Nimber(inv(x)); }
 Nimber square() const { return Nimber(square(x)); }
 Nimber sqrt() const {
  u16 a0= u16(x), a1= u16(x >> 16), a2= u16(x >> 32), a3= x >> 48;
  return a1^= half(a3 ^ a2), a2^= half(a3), a0^= half(a1) ^ half<6>(a3), Nimber((u64(sqrt(a3)) << 48) | (u64(sqrt(a2)) << 32) | (u32(sqrt(a1)) << 16) | sqrt(a0));
 }
 u64 val() const { return x; }
 Nimber pow(u64 k) const { return Nimber(pow(x, k)); }
 u64 log(const Nimber &r) const { return log(x, r.x); }
 bool operator==(const Nimber &r) const { return x == r.x; }
 bool operator!=(const Nimber &r) const { return x != r.x; }
 bool operator<(const Nimber &r) const { return x < r.x; }
 bool operator>(const Nimber &r) const { return x > r.x; }
 bool operator<=(const Nimber &r) const { return x <= r.x; }
 bool operator>=(const Nimber &r) const { return x >= r.x; }
 friend std::ostream &operator<<(std::ostream &os, const Nimber &r) { return os << r.x; }
 friend std::istream &operator>>(std::istream &is, Nimber &r) { return is >> r.x, is; }
};
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 Nimber::init();
 int N, M;
 cin >> N >> M;
 Matrix<Nimber> m(M, N);
 Vector<Nimber> Y(M);
 for (int i= 0; i < M; ++i) {
  int A;
  cin >> A;
  for (int j= 0; j < A; ++j) {
   int B;
   cin >> B, --B;
   m[i][B]= 1;
  }
  cin >> Y[i];
 }
 auto sol= LU_Decomposition(m).linear_equations(Y);
 if (sol) {
  for (int i= 0; i < N; ++i) cout << sol[i] << '\n';
 } else cout << -1 << '\n';
 return 0;
}
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