#753499 (C++17(gcc12)) No.1901 bitwise xor convolution (characteristic 2)

• 問題: No.1901 bitwise xor convolution (characteristic 2)
• ユーザー: NyaanNyaan
• 提出日時: 2022-04-12 21:23:09
• 言語: C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
• 結果: CE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 20,148 bytes
• コンパイル時間: 9,333 ms
• コンパイル使用メモリ: 285,804 KB
• 最終ジャッジ日時: 2025-01-28 17:30:41
• ジャッジサーバーID （参考情報）: judge4 / judge1

コンパイルメッセージ

In file included from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/immintrin.h:39,
                 from main.cpp:9:
/home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/smmintrin.h: In function 'T operator*(const T&, const T&)':
/home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/smmintrin.h:455:1: error: inlining failed in call to 'always_inline' 'long long int _mm_extract_epi64(__m128i, int)': target specific option mismatch
  455 | _mm_extract_epi64 (__m128i __X, const int __N)
      | ^~~~~~~~~~~~~~~~~
main.cpp:795:12: note: called from here
In file included from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/immintrin.h:41:
/home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/wmmintrin.h:116:1: error: inlining failed in call to 'always_inline' '__m128i _mm_clmulepi64_si128(__m128i, __m128i, int)': target specific option mismatch
  116 | _mm_clmulepi64_si128 (__m128i __X, __m128i __Y, const int __I)
      | ^~~~~~~~~~~~~~~~~~~~
main.cpp:794:38: note: called from here
/home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/smmintrin.h:455:1: error: inlining failed in call to 'always_inline' 'long long int _mm_extract_epi64(__m128i, int)': target specific option mismatch
  455 | _mm_extract_epi64 (__m128i __X, const int __N)
      | ^~~~~~~~~~~~~~~~~
main.cpp:795:12: note: called from here
/home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/wmmintrin.h:116:1: error: inlining failed in call to 'always_inline' '__m128i _mm_clmulepi64_si128(__m128i, __m128i, int)': target specific option mismatch
  116 | _mm_clmulepi64_si128 (__m128i __X, __m128i __Y, const int __I)
      | ^~~~~~~~~~~~~~~~~~~~
main.cpp:794:38: note: called from here

ソースコード

/**
 *  date : 2022-04-12 21:23:02
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  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) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

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>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

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);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    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>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}



#define inV(T, v, n) \
  vector<T> v(n);    \
  in(v)

#define inVV(T, v, h, w)                \
  vector<vector<T>> v(h, vector<T>(w)); \
  in(v);

template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

// 区間：半開区間 (ng, ok] または [ok, ng)
template <typename T, typename F>
T binary_search(T ng, T ok, const F& f) {
  if constexpr (is_integral<T>::value == true) {
    while (abs(ok - ng) > 1) {
      T x = (ok + ng) / 2;
      (f(x) ? ok : ng) = x;
    }
    return ok;
  } else {
    for (int iter = 0; iter < 60; iter++) {
      T x = (ok + ng) / 2;
      (f(x) ? ok : ng) = x;
    }
    return ok;
  }
}

// 解区間 (l, r)
template <typename T, typename F>
void ternary_search(T l, T r, const F& f, bool greater = false) {
  if constexpr (is_integral<T>::value == true) {
    while (abs(l - r) > 2) {
      T llr = (l * 2 + r * 1) / 3;
      T lrr = (l * 1 + r * 2) / 3;
      bool flag = f(llr) < f(lrr);
      if (flag != greater) {
        r = lrr;
      } else {
        l = llr;
      }
    }
    return (l + r) / 2;
  } else {
    for (int iter = 0; iter < 80; iter++) {
      T llr = (l * 2 + r * 1) / 3;
      T lrr = (l * 1 + r * 2) / 3;
      bool flag = f(llr) < f(lrr);
      if (flag != greater) {
        r = lrr;
      } else {
        l = llr;
      }
    }
    return (l + r) / 2;
  }
}

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan

// inout
namespace Nyaan {

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;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

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, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

void dump(__int128_t t) {
  if (t == 0) cerr << 0;
  if (t < 0) cerr << '-', t = -t;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

void dump(__uint128_t t) {
  if (t == 0) cerr << 0;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#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 reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#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 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 die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//


using namespace std;

namespace fastio {
static constexpr int SZ = 1 << 17;
char inbuf[SZ], outbuf[SZ];
int in_left = 0, in_right = 0, out_right = 0;

struct Pre {
  char num[40000];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i * 4 + j] = n % 10 + '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  int len = in_right - in_left;
  memmove(inbuf, inbuf + in_left, len);
  in_right = len + fread(inbuf + len, 1, SZ - len, stdin);
  in_left = 0;
}

inline void flush() {
  fwrite(outbuf, 1, out_right, stdout);
  out_right = 0;
}

inline void skip_space() {
  if (in_left + 32 > in_right) load();
  while (inbuf[in_left] <= ' ') in_left++;
}

inline void rd(char& c) {
  if (in_left + 32 > in_right) load();
  c = inbuf[in_left++];
}
template <typename T>
inline void rd(T& x) {
  if (in_left + 32 > in_right) load();
  char c;
  do c = inbuf[in_left++];
  while (c < '-');
  [[maybe_unused]] bool minus = false;
  if constexpr (is_signed<T>::value == true) {
    if (c == '-') minus = true, c = inbuf[in_left++];
  }
  x = 0;
  while (c >= '0') {
    x = x * 10 + (c & 15);
    c = inbuf[in_left++];
  }
  if constexpr (is_signed<T>::value == true) {
    if (minus) x = -x;
  }
}
inline void rd() {}
template <typename Head, typename... Tail>
inline void rd(Head& head, Tail&... tail) {
  rd(head);
  rd(tail...);
}

inline void wt(char c) {
  if (out_right > SZ - 32) flush();
  outbuf[out_right++] = c;
}
inline void wt(bool b) {
  if (out_right > SZ - 32) flush();
  outbuf[out_right++] = b ? '1' : '0';
}
inline void wt(const string &s) {
  if (out_right + s.size() > SZ - 32) flush();
  memcpy(outbuf + out_right, s.data(), sizeof(char) * s.size());
  out_right += s.size();
}
template <typename T>
inline void wt(T x) {
  if (out_right > SZ - 32) flush();
  if (!x) {
    outbuf[out_right++] = '0';
    return;
  }
  if constexpr (is_signed<T>::value == true) {
    if (x < 0) outbuf[out_right++] = '-', x = -x;
  }
  int i = 12;
  char buf[16];
  while (x >= 10000) {
    memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
    x /= 10000;
    i -= 4;
  }
  if (x < 100) {
    if (x < 10) {
      outbuf[out_right] = '0' + x;
      ++out_right;
    } else {
      uint32_t q = (uint32_t(x) * 205) >> 11;
      uint32_t r = uint32_t(x) - q * 10;
      outbuf[out_right] = '0' + q;
      outbuf[out_right + 1] = '0' + r;
      out_right += 2;
    }
  } else {
    if (x < 1000) {
      memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3);
      out_right += 3;
    } else {
      memcpy(outbuf + out_right, pre.num + (x << 2), 4);
      out_right += 4;
    }
  }
  memcpy(outbuf + out_right, buf + i + 4, 12 - i);
  out_right += 12 - i;
}
inline void wt() {}
template <typename Head, typename... Tail>
inline void wt(Head&& head, Tail&&... tail) {
  wt(head);
  wt(forward<Tail>(tail)...);
}
template <typename... Args>
inline void wtn(Args&&... x) {
  wt(forward<Args>(x)...);
  wt('\n');
}

struct Dummy {
  Dummy() { atexit(flush); }
} dummy;

}  // namespace fastio
using fastio::rd;
using fastio::skip_space;
using fastio::wt;
using fastio::wtn;


namespace KaratsubaImpl {
  
template <typename T>
vector<T> naive(const vector<T>& a, const vector<T>& b) {
  if (a.empty() and b.empty()) return {};
  if (a.size() < b.size()) return naive(b, a);
  int s = a.size(), t = b.size();
  vector<T> c(s + t - 1);
  for (int i = 0; i < s; i++) {
    for (int j = 0; j < t; j++) c[i + j] += a[i] * b[j];
  }
  return c;
}

template <typename T>
void add(vector<T>& a, const vector<T>& b) {
  if (a.size() < b.size()) a.resize(b.size());
  for (int i = 0; i < (int)b.size(); i++) a[i] += b[i];
}
template <typename T>
void sub(vector<T>& a, const vector<T>& b) {
  if (a.size() < b.size()) a.resize(b.size());
  for (int i = 0; i < (int)b.size(); i++) a[i] -= b[i];
}

template <typename T>
vector<T> karatsuba(const vector<T>& a, const vector<T>& b) {
  if (a.empty() and b.empty()) return {};
  if (a.size() < b.size()) return karatsuba(b, a);
  if (a.size() < 32) return naive(a, b);
  int d = a.size() / 2;
  vector<T> al{begin(a), begin(a) + d}, au{begin(a) + d, end(a)};
  if ((int)b.size() < d + 10) {
    auto cl = karatsuba(al, b);
    auto cu = karatsuba(au, b);
    vector<T> c(a.size() + b.size() - 1);
    for (int i = 0; i < (int)cl.size(); i++) c[i] = cl[i];
    for (int i = 0; i < (int)cu.size(); i++) c[i + d] += cu[i];
    return c;
  }
  vector<T> bl{begin(b), begin(b) + d}, bu{begin(b) + d, end(b)};
  vector<T> alu{al}, blu{bl};
  add(alu, au), add(blu, bu);
  auto cll = karatsuba(al, bl);
  auto cuu = karatsuba(au, bu);
  auto clu = karatsuba(alu, blu);
  sub(clu, cll), sub(clu, cuu);
  vector<T> c(d);
  copy(begin(clu), end(clu), back_inserter(c));
  c.resize(a.size() + b.size() - 1);
  add(c, cll);
  for (int i = 0; i < (int)cuu.size(); i++) c[i + 2 * d] += cuu[i];
  c.resize(a.size() + b.size() - 1);
  return c;
}

}  // namespace KaratsubaImpl
using KaratsubaImpl::karatsuba;

using namespace Nyaan;

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("pclmul,avx2")


struct T {
  ll x;
  T() : x(0) {}
  T(ll y) : x(y) {}

  friend T operator+(const T& l, const T& r) { return T{l.x ^ r.x}; }
  friend T operator-(const T& l, const T& r) { return T{l.x ^ r.x}; }
  friend T operator*(const T& l, const T& r) {
    __m128i x_ = _mm_set_epi64x(0, l.x);
    __m128i y_ = _mm_set_epi64x(0, r.x);
    __m128i z_ = _mm_clmulepi64_si128(x_, y_, 0);
    return T{_mm_extract_epi64(z_, 0)};
  }
  T operator+=(const T& r) { return *this = *this + r; }
  T operator-=(const T& r) { return *this = *this - r; }
  T operator*=(const T& r) { return *this = *this * r; }
};

vector<T> naive(const vector<T>& a, const vector<T>& b) {
  if (a.empty() and b.empty()) return {};
  if (a.size() < b.size()) return naive(b, a);
  int s = a.size(), t = b.size();
  assert(s == t);
  vector<T> c(s);
  for (int i = 0; i < s; i++) {
    for (int j = 0; j < t; j++) c[i ^ j] += a[i] * b[j];
  }
  return c;
}
void add(vector<T>& a, const vector<T>& b) {
  if (a.size() < b.size()) a.resize(b.size());
  for (int i = 0; i < (int)b.size(); i++) a[i] += b[i];
}

vector<T> karatsuba(const vector<T>& a, const vector<T>& b) {
  if (a.size() < 32) return naive(a, b);
  int d = a.size() / 2;
  vector<T> al{begin(a), begin(a) + d}, au{begin(a) + d, end(a)};
  vector<T> bl{begin(b), begin(b) + d}, bu{begin(b) + d, end(b)};
  vector<T> alu{al}, blu{bl};
  add(alu, au), add(blu, bu);
  auto cll = karatsuba(al, bl);
  auto cuu = karatsuba(au, bu);
  auto clu = karatsuba(alu, blu);
  add(clu, cll), add(clu, cuu);
  add(cll, cuu);
  vector<T> c;
  copy(begin(cll), end(cll), back_inserter(c));
  copy(begin(clu), end(clu), back_inserter(c));
  return c;
}

void Nyaan::solve() {
  int N;
  rd(N);
  V<T> A(1 << N), B(1 << N);

  rep(i, 1 << N) rep(j, 32) {
    int x;
    rd(x);
    A[i].x |= ll(x) << j;
  }
  rep(i, 1 << N) rep(j, 32) {
    int x;
    rd(x);
    B[i].x |= ll(x) << j;
  }

  auto C = karatsuba(A, B);
  rep(i, 1 << N) rep(j, 63) {
    int x = gbit(C[i].x, j);
    wt(x);
    wt(" \n"[j == 62]);
  }
}