library

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:heavy_check_mark: test/1_mytest/nimber_log.test.cpp

Depends on

Code

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

#include "random/base.hpp"
#include "nt/nimber/nimber_log.hpp"

void test_16() {
  FOR(n, 1, 65536) {
    Nimber16 x(n);
    u64 m = nimber_log(x);
    assert(root_16.pow(m) == x);
  }
}

void test_32() {
  FOR(1 << 15) {
    Nimber32 x(RNG_64());
    if (x == 0) continue;
    u64 n = nimber_log(x);
    assert(root_32.pow(n) == x);
  }
}

void test_64() {
  FOR(1 << 15) {
    Nimber64 x(RNG_64());
    if (x == 0) continue;
    u64 n = nimber_log(x);
    assert(root_64.pow(n) == x);
  }
  FOR(1 << 15) {
    Nimber64 x(RNG_64());
    Nimber64 y(RNG_64());
    if (x == 0 || y == 0) continue;
    u64 n = nimber_log(x, y);
    if (n != u64(-1)) assert(x.pow(n) == y);
  }
  FOR(1 << 15) {
    Nimber64 x(RNG_64());
    u64 n = RNG_64();
    Nimber64 y = x.pow(n);
    u64 m = nimber_log(x, y);
    assert(m != u64(-1) && x.pow(m) == y);
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test_16();
  test_32();
  test_64();
  solve();
  return 0;
}
#line 1 "test/1_mytest/nimber_log.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
  vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 3 "test/1_mytest/nimber_log.test.cpp"

#line 2 "random/base.hpp"

u64 RNG_64() {
  static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "nt/nimber/nimber_impl.hpp"
namespace NIM_PRODUCT {
u16 E[65535 * 2 + 7];
u16 L[65536];
u64 S[4][65536];
u64 SR[4][65536];

u16 p16_15(u16 a, u16 b) { return (a && b ? E[u32(L[a]) + L[b] + 3] : 0); }
u16 p16_15_15(u16 a, u16 b) { return (a && b ? E[u32(L[a]) + L[b] + 6] : 0); }
u16 mul_15(u16 a) { return (a ? E[3 + L[a]] : 0); }
u16 mul_15_15(u16 a) { return (a ? E[6 + L[a]] : 0); }
u32 p32_mul_31(u32 a, u32 b) {
  u16 al = a & 65535, ah = a >> 16, bl = b & 65535, bh = b >> 16;
  u16 x = p16_15(al, bl);
  u16 y = p16_15_15(ah, bh);
  u16 z = p16_15(al ^ ah, bl ^ bh);
  return u32(y ^ z) << 16 | mul_15(z ^ x);
}
u32 mul_31(u32 a) {
  u16 al = a & 65535, ah = a >> 16;
  return u32(mul_15(al ^ ah)) << 16 | mul_15_15(ah);
}

u16 prod(u16 a, u16 b) { return (a && b ? E[u32(L[a]) + L[b]] : 0); }
u32 prod(u32 a, u32 b) {
  u16 al = a & 65535, ah = a >> 16, bl = b & 65535, bh = b >> 16;
  u16 c = prod(al, bl);
  return u32(prod(u16(al ^ ah), u16(bl ^ bh)) ^ c) << 16 | (p16_15(ah, bh) ^ c);
}
u64 prod(u64 a, u64 b) {
  u32 al = a & 0xffffffff, ah = a >> 32, bl = b & 0xffffffff, bh = b >> 32;
  u32 c = prod(al, bl);
  return u64(prod(al ^ ah, bl ^ bh) ^ c) << 32 ^ (p32_mul_31(ah, bh) ^ c);
}

u16 square(u16 a) { return S[0][a]; }
u32 square(u32 a) { return S[0][a & 65535] ^ S[1][a >> 16]; }
u64 square(u64 a) { return S[0][a & 65535] ^ S[1][a >> 16 & 65535] ^ S[2][a >> 32 & 65535] ^ S[3][a >> 48 & 65535]; }
u16 sqrt(u16 a) { return SR[0][a]; }
u32 sqrt(u32 a) { return SR[0][a & 65535] ^ SR[1][a >> 16]; }
u64 sqrt(u64 a) { return SR[0][a & 65535] ^ SR[1][a >> 16 & 65535] ^ SR[2][a >> 32 & 65535] ^ SR[3][a >> 48 & 65535]; }

// inv: 2^16 の共役が 2^16+1 であることなどを使う. x^{-1}=y(xy)^{-1} という要領.

u16 inverse(u16 a) { return E[65535 - L[a]]; }
u32 inverse(u32 a) {
  if (a < 65536) return inverse(u16(a));
  u16 al = a & 65535, ah = a >> 16;
  u16 norm = prod(al, al ^ ah) ^ E[L[ah] * 2 + 3];
  int k = 65535 - L[norm];
  al = (al ^ ah ? E[L[al ^ ah] + k] : 0), ah = E[L[ah] + k];
  return al | u32(ah) << 16;
}
u64 inverse(u64 a) {
  if (a <= u32(-1)) return inverse(u32(a));
  u32 al = a & 0xffffffff, ah = a >> 32;
  u32 norm = prod(al, al ^ ah) ^ mul_31(square(ah));
  u32 i = inverse(norm);
  return prod(al ^ ah, i) | u64(prod(ah, i)) << 32;
}

void __attribute__((constructor)) init_nim_table() {
  // 2^16 未満のところについて原始根 10279 での指数対数表を作る

  // 2^k との積

  u16 tmp[] = {10279, 15417, 35722, 52687, 44124, 62628, 15661, 5686, 3862, 1323, 334, 647, 61560, 20636, 4267, 8445};
  u16 nxt[65536];
  FOR(i, 16) {
    FOR(s, 1 << i) { nxt[s | 1 << i] = nxt[s] ^ tmp[i]; }
  }
  E[0] = 1;
  FOR(i, 65534) E[i + 1] = nxt[E[i]];
  memcpy(E + 65535, E, 131070);
  memcpy(E + 131070, E, 14);
  FOR(i, 65535) L[E[i]] = i;
  FOR(t, 4) {
    FOR(i, 16) {
      int k = 16 * t + i;
      u64 X = prod(u64(1) << k, u64(1) << k);
      FOR(s, 1 << i) S[t][s | 1 << i] = S[t][s] ^ X;
    }
  }
  FOR(t, 4) {
    FOR(i, 16) {
      int k = 16 * t + i;
      u64 X = u64(1) << k;
      FOR(63) X = square(X);
      FOR(s, 1 << i) SR[t][s | 1 << i] = SR[t][s] ^ X;
    }
  }
}
} // namespace NIM_PRODUCT

#line 3 "nt/nimber/base.hpp"

template <typename UINT>
struct Nimber {
  using F = Nimber;
  UINT val;

  constexpr Nimber(UINT x = 0) : val(x) {}
  F &operator+=(const F &p) {
    val ^= p.val;
    return *this;
  }
  F &operator-=(const F &p) {
    val ^= p.val;
    return *this;
  }
  F &operator*=(const F &p) {
    val = NIM_PRODUCT::prod(val, p.val);
    return *this;
  }
  F &operator/=(const F &p) {
    *this *= p.inverse();
    return *this;
  }
  F operator-() const { return *this; }
  F operator+(const F &p) const { return F(*this) += p; }
  F operator-(const F &p) const { return F(*this) -= p; }
  F operator*(const F &p) const { return F(*this) *= p; }
  F operator/(const F &p) const { return F(*this) /= p; }
  bool operator==(const F &p) const { return val == p.val; }
  bool operator!=(const F &p) const { return val != p.val; }
  F inverse() const { return NIM_PRODUCT::inverse(val); }
  F pow(u64 n) const {
    assert(n >= 0);
    UINT ret = 1, mul = val;
    while (n > 0) {
      if (n & 1) ret = NIM_PRODUCT::prod(ret, mul);
      mul = NIM_PRODUCT::square(mul);
      n >>= 1;
    }
    return F(ret);
  }
  F square() { return F(NIM_PRODUCT::square(val)); }
  F sqrt() { return F(NIM_PRODUCT::sqrt(val)); }
};

#ifdef FASTIO
template <typename T>
void rd(Nimber<T> &x) {
  fastio::rd(x.val);
}
template <typename T>
void wt(Nimber<T> &x) {
  fastio::wt(x.val);
}
#endif

using Nimber16 = Nimber<u16>;
using Nimber32 = Nimber<u32>;
using Nimber64 = Nimber<u64>;
#line 2 "ds/hashmap.hpp"

// u64 -> Val

template <typename Val>
struct HashMap {
  // n は入れたいものの個数で ok

  HashMap(u32 n = 0) { build(n); }
  void build(u32 n) {
    u32 k = 8;
    while (k < n * 2) k *= 2;
    cap = k / 2, mask = k - 1;
    key.resize(k), val.resize(k), used.assign(k, 0);
  }

  // size を保ったまま. size=0 にするときは build すること.

  void clear() {
    used.assign(len(used), 0);
    cap = (mask + 1) / 2;
  }
  int size() { return len(used) / 2 - cap; }

  int index(const u64& k) {
    int i = 0;
    for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {}
    return i;
  }

  Val& operator[](const u64& k) {
    if (cap == 0) extend();
    int i = index(k);
    if (!used[i]) { used[i] = 1, key[i] = k, val[i] = Val{}, --cap; }
    return val[i];
  }

  Val get(const u64& k, Val default_value) {
    int i = index(k);
    return (used[i] ? val[i] : default_value);
  }

  bool count(const u64& k) {
    int i = index(k);
    return used[i] && key[i] == k;
  }

  // f(key, val)

  template <typename F>
  void enumerate_all(F f) {
    FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
  }

private:
  u32 cap, mask;
  vc<u64> key;
  vc<Val> val;
  vc<bool> used;

  u64 hash(u64 x) {
    static const u64 FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
    x += FIXED_RANDOM;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return (x ^ (x >> 31)) & mask;
  }

  void extend() {
    vc<pair<u64, Val>> dat;
    dat.reserve(len(used) / 2 - cap);
    FOR(i, len(used)) {
      if (used[i]) dat.eb(key[i], val[i]);
    }
    build(2 * len(dat));
    for (auto& [a, b]: dat) (*this)[a] = b;
  }
};
#line 2 "mod/crt3.hpp"

constexpr u32 mod_pow_constexpr(u64 a, u64 n, u32 mod) {
  a %= mod;
  u64 res = 1;
  FOR(32) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod, n /= 2;
  }
  return res;
}

template <typename T, u32 p0, u32 p1>
T CRT2(u64 a0, u64 a1) {
  static_assert(p0 < p1);
  static constexpr u64 x0_1 = mod_pow_constexpr(p0, p1 - 2, p1);
  u64 c = (a1 - a0 + p1) * x0_1 % p1;
  return a0 + c * p0;
}

template <typename T, u32 p0, u32 p1, u32 p2>
T CRT3(u64 a0, u64 a1, u64 a2) {
  static_assert(p0 < p1 && p1 < p2);
  static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);
  static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
  static constexpr u64 p01 = u64(p0) * p1;
  u64 c = (a1 - a0 + p1) * x1 % p1;
  u64 ans_1 = a0 + c * p0;
  c = (a2 - ans_1 % p2 + p2) * x2 % p2;
  return T(ans_1) + T(c) * T(p01);
}

template <typename T, u32 p0, u32 p1, u32 p2, u32 p3>
T CRT4(u64 a0, u64 a1, u64 a2, u64 a3) {
  static_assert(p0 < p1 && p1 < p2 && p2 < p3);
  static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);
  static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
  static constexpr u64 x3 = mod_pow_constexpr(u64(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);
  static constexpr u64 p01 = u64(p0) * p1;
  u64 c = (a1 - a0 + p1) * x1 % p1;
  u64 ans_1 = a0 + c * p0;
  c = (a2 - ans_1 % p2 + p2) * x2 % p2;
  u128 ans_2 = ans_1 + c * static_cast<u128>(p01);
  c = (a3 - ans_2 % p3 + p3) * x3 % p3;
  return T(ans_2) + T(c) * T(p01) * T(p2);
}

template <typename T, u32 p0, u32 p1, u32 p2, u32 p3, u32 p4>
T CRT5(u64 a0, u64 a1, u64 a2, u64 a3, u64 a4) {
  static_assert(p0 < p1 && p1 < p2 && p2 < p3 && p3 < p4);
  static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);
  static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
  static constexpr u64 x3 = mod_pow_constexpr(u64(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);
  static constexpr u64 x4 = mod_pow_constexpr(u64(p0) * p1 % p4 * p2 % p4 * p3 % p4, p4 - 2, p4);
  static constexpr u64 p01 = u64(p0) * p1;
  static constexpr u64 p23 = u64(p2) * p3;
  u64 c = (a1 - a0 + p1) * x1 % p1;
  u64 ans_1 = a0 + c * p0;
  c = (a2 - ans_1 % p2 + p2) * x2 % p2;
  u128 ans_2 = ans_1 + c * static_cast<u128>(p01);
  c = static_cast<u64>(a3 - ans_2 % p3 + p3) * x3 % p3;
  u128 ans_3 = ans_2 + static_cast<u128>(c * p2) * p01;
  c = static_cast<u64>(a4 - ans_3 % p4 + p4) * x4 % p4;
  return T(ans_3) + T(c) * T(p01) * T(p23);
}
#line 4 "nt/nimber/nimber_log.hpp"

// primitive root
const Nimber64 root_64 = u64(1) << 32 | 6;
const Nimber32 root_32 = 2147483651;
const Nimber16 root_16 = 41899;

u64 nimber_log(Nimber16 x) {
  assert(x != 0);
  u32 ans = u32(37991) * NIM_PRODUCT::L[x.val];
  return ans % 65535;
}

u64 nimber_log(Nimber32 x) {
  using F = Nimber32;
  assert(x != 0);
  static HashMap<u32> MP(330);
  static F g = 0;
  if (len(MP) == 0) {
    // build
    g = root_32.pow(65535); // 65537 乗根
    F gg = g.pow(200);
    F pow = 1;
    FOR(i, 330) MP[pow.val] = i, pow *= gg;
  }
  u64 a = [&]() -> u32 {
    F x1 = x.pow(65535);
    FOR(i, 200) {
      u32 k = MP.get(x1.val, -1);
      if (k != u32(-1)) { return (65537 + 200 * k - i) % 65537; }
      x1 *= g;
    }
    assert(0);
    return 0;
  }();
  u64 b = nimber_log(Nimber16(x.pow(65537).val));
  return CRT2<u64, 65535, 65537>(b, a);
}

u64 nimber_log(Nimber64 x) {
  using F = Nimber64;
  assert(x != 0);
  const u64 mod1 = u32(-1);
  const u64 mod2 = mod1 + 2;
  const u32 p1 = 641;
  const u32 p2 = 6700417;
  static HashMap<u32> MP1(3400);
  static HashMap<u32> MP2(641);
  static F g1, g2;
  if (len(MP1) == 0) {
    g1 = root_64.pow(mod1 * p1); // p2 乗根
    g2 = root_64.pow(mod1 * p2); // p1 乗根
    F gg = g1.pow(2000);
    F pow = 1;
    FOR(i, 3400) MP1[pow.val] = i, pow *= gg;
    pow = 1;
    FOR(i, 641) MP2[pow.val] = i, pow *= g2;
  }
  u64 a1 = [&]() -> u64 {
    F x1 = x.pow(mod1 * p1);
    FOR(i, 2000) {
      u32 k = MP1.get(x1.val, -1);
      if (k != u32(-1)) { return (p2 + 2000 * k - i) % p2; }
      x1 *= g1;
    }
    assert(0);
    return 0;
  }();
  u64 a2 = MP2[x.pow(mod1 * p2).val];
  u64 b = nimber_log(Nimber32(x.pow(mod2).val));
  u64 a = CRT2<u64, p1, p2>(a2, a1);
  u128 ans = u128(a) * (u64(-1) - mod1) + u128(b) * mod2;
  if (ans & 1) ans += u64(-1);
  return (ans / 2) % u64(-1);
}

// 最小解. ちょうど -1 を false の意味に使える.
template <typename F>
u64 nimber_log(F x, F y) {
  u64 X = nimber_log(x), Y = nimber_log(y);
  // X*n = Y mod (2^64-1)
  u64 mod = -1;
  u64 a = X, b = mod;
  i128 u = 1, v = 0, t;
  while (b > 0) {
    t = a / b;
    swap(a -= t * b, b), swap(u -= t * v, v);
  }
  if (Y % a != 0) return -1;
  if (u < 0) u += mod;
  return (Y / a) * u % (mod / a);
}
#line 6 "test/1_mytest/nimber_log.test.cpp"

void test_16() {
  FOR(n, 1, 65536) {
    Nimber16 x(n);
    u64 m = nimber_log(x);
    assert(root_16.pow(m) == x);
  }
}

void test_32() {
  FOR(1 << 15) {
    Nimber32 x(RNG_64());
    if (x == 0) continue;
    u64 n = nimber_log(x);
    assert(root_32.pow(n) == x);
  }
}

void test_64() {
  FOR(1 << 15) {
    Nimber64 x(RNG_64());
    if (x == 0) continue;
    u64 n = nimber_log(x);
    assert(root_64.pow(n) == x);
  }
  FOR(1 << 15) {
    Nimber64 x(RNG_64());
    Nimber64 y(RNG_64());
    if (x == 0 || y == 0) continue;
    u64 n = nimber_log(x, y);
    if (n != u64(-1)) assert(x.pow(n) == y);
  }
  FOR(1 << 15) {
    Nimber64 x(RNG_64());
    u64 n = RNG_64();
    Nimber64 y = x.pow(n);
    u64 m = nimber_log(x, y);
    assert(m != u64(-1) && x.pow(m) == y);
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test_16();
  test_32();
  test_64();
  solve();
  return 0;
}
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