verify/verify-yosupo-math/yosupo-nim-product.test.cpp

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Last update: 2024-05-03 23:21:26+09:00
Problem: https://judge.yosupo.jp/problem/nim_product_64

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/nim_product_64"

#include "../../template/template.hpp"
//
#include "../../math/nimber.hpp"
#include "../../misc/fastio.hpp"

using namespace Nyaan;
void Nyaan::solve() {
  int T;
  rd(T);
  rep(i, T) {
    uint64_t a, b;
    rd(a, b);
    wtn(NimberImpl::product64(a, b));
  }
}

#line 1 "verify/verify-yosupo-math/yosupo-nim-product.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/nim_product_64"

#line 2 "template/template.hpp"
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
#line 1 "template/util.hpp"
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>
using minpq = priority_queue<T, vector<T>, greater<T>>;

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(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan
#line 58 "template/template.hpp"

// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(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
#line 61 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
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...);
}

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

}  // namespace Nyaan
#line 64 "template/template.hpp"

// debug
#line 1 "template/debug.hpp"
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(std::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

#ifdef NyaanLocal
#define trc2(...)                           \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"

// macro
#line 1 "template/macro.hpp"
#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)
#line 70 "template/template.hpp"

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-yosupo-math/yosupo-nim-product.test.cpp"
//
#line 2 "math/nimber.hpp"

#line 2 "math/garner.hpp"

// input  : a, M (0 < a < M)
// output : pair(g, x) s.t. g = gcd(a, M), xa = g (mod M), 0 <= x < b/g
template <typename uint>
pair<uint, uint> gcd_inv(uint a, uint M) {
  assert(M != 0 && 0 < a);
  a %= M;
  uint b = M, s = 1, t = 0;
  while (true) {
    if (a == 0) return {b, t + M};
    t -= b / a * s;
    b %= a;
    if (b == 0) return {a, s};
    s -= a / b * t;
    a %= b;
  }
}

// 入力 : 0 <= rem[i] < mod[i], 1 <= mod[i]
// 存在するとき   : return {rem, mod}
// 存在しないとき : return {0, 0}
template <typename T, typename U>
pair<unsigned long long, unsigned long long> garner(const vector<T>& rem,
                                                    const vector<U>& mod) {
  assert(rem.size() == mod.size());
  using u64 = unsigned long long;
  u64 r0 = 0, m0 = 1;
  for (int i = 0; i < (int)rem.size(); i++) {
    assert(1 <= mod[i]);
    assert(0 <= rem[i] && rem[i] < mod[i]);
    u64 m1 = mod[i], r1 = rem[i] % m1;
    if (m0 < m1) swap(r0, r1), swap(m0, m1);
    if (m0 % m1 == 0) {
      if (r0 % m1 != r1) return {0, 0};
      continue;
    }
    u64 g, im;
    tie(g, im) = gcd_inv(m0, m1);
    u64 y = r0 < r1 ? r1 - r0 : r0 - r1;
    if (y % g != 0) return {0, 0};
    u64 u1 = m1 / g;
    y = y / g % u1;
    if (r0 > r1 && y != 0) y = u1 - y;
    u64 x = y * im % u1;
    r0 += x * m0;
    m0 *= u1;
  }
  return {r0, m0};
}

/**
 * @brief Garner's algorithm
 */
#line 4 "math/nimber.hpp"

namespace NimberImpl {
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;

struct calc8 {
  u16 dp[1 << 8][1 << 8];
  constexpr calc8() : dp() {
    dp[0][0] = dp[0][1] = dp[1][0] = 0;
    dp[1][1] = 1;
    for (int e = 1; e <= 3; e++) {
      int p = 1 << e, q = p >> 1;
      u16 ep = 1u << p, eq = 1u << q;
      for (u16 i = 0; i < ep; i++) {
        for (u16 j = i; j < ep; j++) {
          if (i < eq && j < eq) continue;
          if (min(i, j) <= 1u) {
            dp[i][j] = dp[j][i] = i * j;
            continue;
          }
          u16 iu = i >> q, il = i & (eq - 1);
          u16 ju = j >> q, jl = j & (eq - 1);
          u16 u = dp[iu][ju], l = dp[il][jl];
          u16 ul = dp[iu ^ il][ju ^ jl];
          u16 uq = dp[u][eq >> 1];
          dp[i][j] = ((ul ^ l) << q) ^ uq ^ l;
          dp[j][i] = dp[i][j];
        }
      }
    }
  }
} constexpr c8;

struct calc16 {
  static constexpr u16 proot = 10279;
  static constexpr u32 ppoly = 92191;
  static constexpr int order = 65535;

  u16 base[16], exp[(1 << 18) + 100];
  int log[1 << 16];

 private:
  constexpr u16 d(u32 x) { return (x << 1) ^ (x < 32768u ? 0 : ppoly); }

  constexpr u16 naive(u16 i, u16 j) {
    if (min(i, j) <= 1u) return i * j;
    u16 q = 8, eq = 1u << 8;
    u16 iu = i >> q, il = i & (eq - 1);
    u16 ju = j >> q, jl = j & (eq - 1);
    u16 u = c8.dp[iu][ju];
    u16 l = c8.dp[il][jl];
    u16 ul = c8.dp[iu ^ il][ju ^ jl];
    u16 uq = c8.dp[u][eq >> 1];
    return ((ul ^ l) << q) ^ uq ^ l;
  }

 public:
  constexpr calc16() : base(), exp(), log() {
    base[0] = 1;
    for (int i = 1; i < 16; i++) base[i] = naive(base[i - 1], proot);
    exp[0] = 1;
    for (int i = 1; i < order; i++) exp[i] = d(exp[i - 1]);
    u16* pre = exp + order + 1;
    pre[0] = 0;
    for (int b = 0; b < 16; b++) {
      int is = 1 << b, ie = is << 1;
      for (int i = is; i < ie; i++) pre[i] = pre[i - is] ^ base[b];
    }
    for (int i = 0; i < order; i++) exp[i] = pre[exp[i]], log[exp[i]] = i;

    int ie = 2 * order + 30;
    for (int i = order; i < ie; i++) exp[i] = exp[i - order];
    for (unsigned int i = ie; i < sizeof(exp) / sizeof(u16); i++) exp[i] = 0;
    log[0] = ie + 1;
  }

  constexpr u16 prod(u16 i, u16 j) const { return exp[log[i] + log[j]]; }

  // exp[3] = 2^{15} = 32768
  constexpr u16 Hprod(u16 i, u16 j) const { return exp[log[i] + log[j] + 3]; }
  constexpr u16 H(u16 i) const { return exp[log[i] + 3]; }
  constexpr u16 H2(u16 i) const { return exp[log[i] + 6]; }
} constexpr c16;

u16 product16(u16 i, u16 j) { return c16.prod(i, j); }

constexpr u32 product32(u32 i, u32 j) {
  u16 iu = i >> 16, il = i & 65535;
  u16 ju = j >> 16, jl = j & 65535;
  u16 l = c16.prod(il, jl);
  u16 ul = c16.prod(iu ^ il, ju ^ jl);
  u16 uq = c16.Hprod(iu, ju);
  return (u32(ul ^ l) << 16) ^ uq ^ l;
}

// (+ : xor, x : nim product, * : integer product)
// i x j
// = (iu x ju + il x ju + iu x ji) * 2^{16}
// + (iu x ju x 2^{15}) + il x jl
// (assign ju = 2^{15}, jl = 0)
// = ((iu + il) x 2^{15}) * 2^{16} + (iu x 2^{15} x 2^{15})
constexpr u32 H(u32 i) {
  u16 iu = i >> 16;
  u16 il = i & 65535;
  return (u32(c16.H(iu ^ il)) << 16) ^ c16.H2(iu);
}

constexpr u64 product64(u64 i, u64 j) {
  u32 iu = i >> 32, il = i & u32(-1);
  u32 ju = j >> 32, jl = j & u32(-1);
  u32 l = product32(il, jl);
  u32 ul = product32(iu ^ il, ju ^ jl);
  u32 uq = H(product32(iu, ju));
  return (u64(ul ^ l) << 32) ^ uq ^ l;
}
}  // namespace NimberImpl

template <typename uint, uint (*prod)(uint, uint)>
struct NimberBase {
  using N = NimberBase;
  uint x;
  NimberBase() : x(0) {}
  NimberBase(uint _x) : x(_x) {}
  static N id0() { return {}; }
  static N id1() { return {1}; }

  N& operator+=(const N& p) {
    x ^= p.x;
    return *this;
  }
  N& operator-=(const N& p) {
    x ^= p.x;
    return *this;
  }
  N& operator*=(const N& p) {
    x = prod(x, p.x);
    return *this;
  }
  N operator+(const N& p) const { return x ^ p.x; }
  N operator-(const N& p) const { return x ^ p.x; }
  N operator*(const N& p) const { return prod(x, p.x); }
  bool operator==(const N& p) const { return x == p.x; }
  bool operator!=(const N& p) const { return x != p.x; }
  N pow(uint64_t n) const {
    N a = *this, r = 1;
    for (; n; a *= a, n >>= 1)
      if (n & 1) r *= a;
    return r;
  }
  friend ostream& operator<<(ostream& os, const N& p) { return os << p.x; }

  // calculate log_a (b)
  uint discrete_logarithm(N y) const {
    assert(x != 0 && y != 0);
    vector<uint> rem, mod;
    for (uint p : {3, 5, 17, 257, 641, 65537, 6700417}) {
      if (uint(-1) % p) continue;
      uint q = uint(-1) / p;
      uint STEP = 1;
      while (4 * STEP * STEP < p) STEP *= 2;
      // a^m = z を満たす 1 以上の整数 m を返す
      auto inside = [&](N a, N z) -> uint {
        unordered_map<uint, int> mp;
        N big = 1, now = 1;  // x^m
        for (int i = 0; i < int(STEP); i++) {
          mp[z.x] = i, z *= a, big *= a;
        }
        for (int step = 0; step < int(p + 10); step += STEP) {
          now *= big;
          if (mp.find(now.x) != mp.end()) return (step + STEP) - mp[now.x];
        }
        return uint(-1);
      };
      N xq = (*this).pow(q), yq = y.pow(q);
      if (xq == 1 and yq == 1) continue;
      if (xq == 1 and yq != 1) return uint(-1);
      uint res = inside(xq, yq);
      if (res == uint(-1)) return uint(-1);
      rem.push_back(res % p);
      mod.push_back(p);
    }
    return garner(rem, mod).first;
  }

  uint is_primitive_root() const {
    if (x == 0) return false;
    for (uint p : {3, 5, 17, 257, 641, 65537, 6700417}) {
      if (uint(-1) % p != 0) continue;
      if ((*this).pow(uint(-1) / p) == 1) return false;
    }
    return true;
  }
};

using Nimber16 = NimberBase<uint16_t, NimberImpl::product16>;
using Nimber32 = NimberBase<uint32_t, NimberImpl::product32>;
using Nimber64 = NimberBase<uint64_t, NimberImpl::product64>;
using Nimber = Nimber64;

/**
 * @brief Nim Product
 * @docs docs/math/nimber.md
 */
#line 2 "misc/fastio.hpp"

#line 8 "misc/fastio.hpp"

using namespace std;

#line 2 "internal/internal-type-traits.hpp"

#line 4 "internal/internal-type-traits.hpp"
using namespace std;

namespace internal {
template <typename T>
using is_broadly_integral =
    typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
                               is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_signed =
    typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_unsigned =
    typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

#define ENABLE_VALUE(x) \
  template <typename T> \
  constexpr bool x##_v = x<T>::value;

ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                   \
  template <class, class = void>                               \
  struct has_##var : false_type {};                            \
  template <class T>                                           \
  struct has_##var<T, void_t<typename T::var>> : true_type {}; \
  template <class T>                                           \
  constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                     \
  template <class, class = void>                                \
  struct has_##var : false_type {};                             \
  template <class T>                                            \
  struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
  template <class T>                                            \
  constexpr auto has_##var##_v = has_##var<T>::value;

}  // namespace internal
#line 12 "misc/fastio.hpp"

namespace fastio {
static constexpr int SZ = 1 << 17;
static constexpr int offset = 64;
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;

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;
}
void flush() {
  fwrite(outbuf, 1, out_right, stdout);
  out_right = 0;
}
void skip_space() {
  if (in_left + offset > in_right) load();
  while (inbuf[in_left] <= ' ') in_left++;
}

void single_read(char& c) {
  if (in_left + offset > in_right) load();
  skip_space();
  c = inbuf[in_left++];
}
void single_read(string& S) {
  skip_space();
  while (true) {
    if (in_left == in_right) load();
    int i = in_left;
    for (; i != in_right; i++) {
      if (inbuf[i] <= ' ') break;
    }
    copy(inbuf + in_left, inbuf + i, back_inserter(S));
    in_left = i;
    if (i != in_right) break;
  }
}
template <typename T,
          enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr>
void single_read(T& x) {
  if (in_left + offset > in_right) load();
  skip_space();
  char c = inbuf[in_left++];
  [[maybe_unused]] bool minus = false;
  if constexpr (internal::is_broadly_signed_v<T>) {
    if (c == '-') minus = true, c = inbuf[in_left++];
  }
  x = 0;
  while (c >= '0') {
    x = x * 10 + (c & 15);
    c = inbuf[in_left++];
  }
  if constexpr (internal::is_broadly_signed_v<T>) {
    if (minus) x = -x;
  }
}
void rd() {}
template <typename Head, typename... Tail>
void rd(Head& head, Tail&... tail) {
  single_read(head);
  rd(tail...);
}

void single_write(const char& c) {
  if (out_right > SZ - offset) flush();
  outbuf[out_right++] = c;
}
void single_write(const bool& b) {
  if (out_right > SZ - offset) flush();
  outbuf[out_right++] = b ? '1' : '0';
}
void single_write(const string& S) {
  flush(), fwrite(S.data(), 1, S.size(), stdout);
}
void single_write(const char* p) { flush(), fwrite(p, 1, strlen(p), stdout); }
template <typename T,
          enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr>
void single_write(const T& _x) {
  if (out_right > SZ - offset) flush();
  if (_x == 0) {
    outbuf[out_right++] = '0';
    return;
  }
  T x = _x;
  if constexpr (internal::is_broadly_signed_v<T>) {
    if (x < 0) outbuf[out_right++] = '-', x = -x;
  }
  constexpr int buffer_size = sizeof(T) * 10 / 4;
  char buf[buffer_size];
  int i = buffer_size;
  while (x >= 10000) {
    i -= 4;
    memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
    x /= 10000;
  }
  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, buffer_size - i);
  out_right += buffer_size - i;
}
void wt() {}
template <typename Head, typename... Tail>
void wt(const Head& head, const Tail&... tail) {
  single_write(head);
  wt(std::forward<const Tail>(tail)...);
}
template <typename... Args>
void wtn(const Args&... x) {
  wt(std::forward<const 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;
#line 7 "verify/verify-yosupo-math/yosupo-nim-product.test.cpp"

using namespace Nyaan;
void Nyaan::solve() {
  int T;
  rd(T);
  rep(i, T) {
    uint64_t a, b;
    rd(a, b);
    wtn(NimberImpl::product64(a, b));
  }
}

Nyaan's Library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/verify-yosupo-math/yosupo-nim-product.test.cpp

Depends on

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