verify/math/UNIT_util.test.cpp

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Last update: 2026-06-28 19:44:47+09:00
Problem: https://judge.yosupo.jp/problem/aplusb

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

#include "template/template.hpp"
#include "math/util.hpp"

void test_division() {
  rep(a, -100, 101) rep(b, -100, 101) {
    if (b == 0) continue;
    int m = abs(b);
    int r = Math::safe_mod(a, b);
    assert(0 <= r && r < m);
    assert(((b < 0 ? -a : a) - r) % m == 0);

    int f = Math::floor(a, b);
    int c = Math::ceil(a, b);
    long double v = (long double)a / b;
    assert(f <= v && v < f + 1);
    assert(c - 1 < v && v <= c);
  }
}

void test_roots() {
  auto check_sqrt = [](long long n) {
    long long x = Math::isqrt(n);
    assert((__int128)x * x <= n);
    assert((__int128)(x + 1) * (x + 1) > n);
  };
  rep(n, 0, 100000) check_sqrt(n);
  for (long long n : {1000000000000LL, 9223372036854775807LL}) check_sqrt(n);

  rep(n, 0, 10000) rep(k, 1, 11) {
    long long x = Math::floor_root(n, k);
    auto leq = [&](long long a) {
      __int128 p = 1;
      rep(i, 0, k) p *= a;
      return p <= n;
    };
    assert(leq(x));
    assert(!leq(x + 1));
  }
  assert(Math::floor_root(9223372036854775807LL, 2) == 3037000499LL);
}

void test_number_theory() {
  rep(a, -100, 101) rep(b, -100, 101) {
    if (a == 0 && b == 0) continue;
    long long x, y;
    long long g = Math::ext_gcd((long long)a, (long long)b, x, y);
    assert(g == gcd(abs(a), abs(b)));
    assert((long long)a * x + (long long)b * y == g);
  }

  rep(m, 2, 200) rep(a, 1, m) {
    if (gcd(a, m) == 1) assert(a * Math::inv_mod(a, m) % m == 1);
  }
  rep(x, -20, 21) rep(n, 0, 20) rep(m, 1, 50) {
    long long expected = 1 % m;
    rep(i, 0, n) expected = expected * Math::safe_mod(x, m) % m;
    assert(Math::pow_mod(x, n, m) == expected);
  }
  rep(n, 0, 1000) {
    bool prime = n >= 2;
    for (int d = 2; d * d <= n; d++) prime &= n % d != 0;
    assert(Math::is_prime_constexpr(n) == prime);
  }
}

int main() {
  test_division();
  test_roots();
  test_number_theory();

  int a, b;
  in(a, b);
  out(a + b);
}

#line 1 "verify/math/UNIT_util.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"

#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <class T, class S = T>
S SUM(const vector<T>& a) {
  return accumulate(ALL(a), S(0));
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"

#line 2 "template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

ostream& operator<<(ostream& os, __uint128_t x) {
  char buf[40];
  size_t k = 0;
  while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
  if (k == 0) buf[k++] = '0';
  while (k) os << buf[--k];
  return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
  return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
  for (auto& v : a) is >> v;
  return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

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...);
}

namespace IO {
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    u -= offset, v -= offset;
    g[u].push_back(v);
    if (!directed) g[v].push_back(u);
  }
  return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<pair<int, T>>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    T w;
    cin >> u >> v >> w;
    u -= offset, v -= offset;
    g[u].push_back({v, w});
    if (!directed) g[v].push_back({u, w});
  }
  return g;
}
}  // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
  return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
  return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 1; i < n; i++) {
    int p;
    cin >> p;
    p -= offset;
    if (to_root) g[i].push_back(p);
    if (to_leaf) g[p].push_back(i);
  }
  return g;
}
}  // namespace Tree
}  // namespace IO
#line 10 "template/template.hpp"

#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int i, T name) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "math/util.hpp"

namespace Math {
template <class T>
T safe_mod(T a, T b) {
  assert(b != 0);
  if (b < 0) a = -a, b = -b;
  a %= b;
  return a >= 0 ? a : a + b;
}
template <class T>
T floor(T a, T b) {
  assert(b != 0);
  if (b < 0) a = -a, b = -b;
  return a >= 0 ? a / b : (a + 1) / b - 1;
}
template <class T>
T ceil(T a, T b) {
  assert(b != 0);
  if (b < 0) a = -a, b = -b;
  return a > 0 ? (a - 1) / b + 1 : a / b;
}
long long isqrt(long long n) {
  if (n <= 0) return 0;
  long long x = sqrt(n);
  while ((__int128)(x + 1) * (x + 1) <= n) x++;
  while ((__int128)x * x > n) x--;
  return x;
}
long long floor_root(long long n, int k) {
  assert(n >= 0);
  if (n == 0) return 0;
  assert(k >= 1);
  if (k == 1) return n;
  if (k > 64) return 1;
  long long x = round(pow((long double)n, 1.0L / k));
  auto check = [&](long long a) {
    if (a <= 0) return true;
    __int128_t p = 1;
    for (int i = 0; i < k; ++i)
      if ((p *= a) > n) return false;
    return true;
  };
  while (check(x + 1)) x++;
  while (!check(x)) x--;
  return x;
}
// return g=gcd(a,b)
// a*x+b*y=g
// - b!=0 -> 0<=x<|b|/g
// - b=0  -> ax=g
template <class T>
T ext_gcd(T a, T b, T& x, T& y) {
  T a0 = a, b0 = b;
  bool sgn_a = a < 0, sgn_b = b < 0;
  if (sgn_a) a = -a;
  if (sgn_b) b = -b;
  if (b == 0) {
    x = sgn_a ? -1 : 1;
    y = 0;
    return a;
  }
  T x00 = 1, x01 = 0, x10 = 0, x11 = 1;
  while (b != 0) {
    T q = a / b, r = a - b * q;
    x00 -= q * x01;
    x10 -= q * x11;
    swap(x00, x01);
    swap(x10, x11);
    a = b, b = r;
  }
  x = x00, y = x10;
  if (sgn_a) x = -x;
  if (sgn_b) y = -y;
  if (b0 != 0) {
    a0 /= a, b0 /= a;
    if (b0 < 0) a0 = -a0, b0 = -b0;
    T q = x >= 0 ? x / b0 : (x + 1) / b0 - 1;
    x -= b0 * q;
    y += a0 * q;
  }
  return a;
}
constexpr long long inv_mod(long long x, long long m) {
  x %= m;
  if (x < 0) x += m;
  long long a = m, b = x;
  long long y0 = 0, y1 = 1;
  while (b > 0) {
    long long q = a / b;
    swap(a -= q * b, b);
    swap(y0 -= q * y1, y1);
  }
  if (y0 < 0) y0 += m / a;
  return y0;
}
long long pow_mod(long long x, long long n, long long m) {
  if (m == 1) return 0;
  x = (x % m + m) % m;
  long long y = 1;
  while (n) {
    if (n & 1) y = y * x % m;
    x = x * x % m;
    n >>= 1;
  }
  return y;
}
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
  if (m == 1) return 0;
  unsigned int _m = (unsigned int)(m);
  unsigned long long r = 1;
  unsigned long long y = x % m;
  if (y >= m) y += m;
  while (n) {
    if (n & 1) r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}
constexpr bool is_prime_constexpr(int n) {
  if (n <= 1) return false;
  if (n == 2 || n == 7 || n == 61) return true;
  if (n % 2 == 0) return false;
  long long d = n - 1;
  while (d % 2 == 0) d /= 2;
  constexpr long long bases[3] = {2, 7, 61};
  for (long long a : bases) {
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
};  // namespace Math
#line 5 "verify/math/UNIT_util.test.cpp"

void test_division() {
  rep(a, -100, 101) rep(b, -100, 101) {
    if (b == 0) continue;
    int m = abs(b);
    int r = Math::safe_mod(a, b);
    assert(0 <= r && r < m);
    assert(((b < 0 ? -a : a) - r) % m == 0);

    int f = Math::floor(a, b);
    int c = Math::ceil(a, b);
    long double v = (long double)a / b;
    assert(f <= v && v < f + 1);
    assert(c - 1 < v && v <= c);
  }
}

void test_roots() {
  auto check_sqrt = [](long long n) {
    long long x = Math::isqrt(n);
    assert((__int128)x * x <= n);
    assert((__int128)(x + 1) * (x + 1) > n);
  };
  rep(n, 0, 100000) check_sqrt(n);
  for (long long n : {1000000000000LL, 9223372036854775807LL}) check_sqrt(n);

  rep(n, 0, 10000) rep(k, 1, 11) {
    long long x = Math::floor_root(n, k);
    auto leq = [&](long long a) {
      __int128 p = 1;
      rep(i, 0, k) p *= a;
      return p <= n;
    };
    assert(leq(x));
    assert(!leq(x + 1));
  }
  assert(Math::floor_root(9223372036854775807LL, 2) == 3037000499LL);
}

void test_number_theory() {
  rep(a, -100, 101) rep(b, -100, 101) {
    if (a == 0 && b == 0) continue;
    long long x, y;
    long long g = Math::ext_gcd((long long)a, (long long)b, x, y);
    assert(g == gcd(abs(a), abs(b)));
    assert((long long)a * x + (long long)b * y == g);
  }

  rep(m, 2, 200) rep(a, 1, m) {
    if (gcd(a, m) == 1) assert(a * Math::inv_mod(a, m) % m == 1);
  }
  rep(x, -20, 21) rep(n, 0, 20) rep(m, 1, 50) {
    long long expected = 1 % m;
    rep(i, 0, n) expected = expected * Math::safe_mod(x, m) % m;
    assert(Math::pow_mod(x, n, m) == expected);
  }
  rep(n, 0, 1000) {
    bool prime = n >= 2;
    for (int d = 2; d * d <= n; d++) prime &= n % d != 0;
    assert(Math::is_prime_constexpr(n) == prime);
  }
}

int main() {
  test_division();
  test_roots();
  test_number_theory();

  int a, b;
  in(a, b);
  out(a + b);
}