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

Depends on

Code

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

#include "my_template.hpp"

#include "random/base.hpp"
#include "ds/wavelet_matrix/wavelet_matrix.hpp"
#include "ds/static_range_product_group.hpp"
#include "ds/segtree/segtree.hpp"
#include "alg/monoid/min.hpp"

template <bool SMALL_Y, typename SEGTREE>
void test(int N) {
  int MAX = RNG(2, 1 << 10);
  vc<int> A(N);
  vc<int> X(N);
  FOR(i, N) X[i] = RNG(MAX);
  FOR(i, N) A[i] = RNG(MAX);

  Wavelet_Matrix<int, false, SEGTREE> WM(A, X);
  using Mono = typename SEGTREE::MX;

  int Q = 100;
  FOR(Q) {
    int L = RNG(0, max(1, N));
    int R = RNG(0, max(1, N + 1));
    if (L > R) swap(L, R);
    int lo = RNG(0, MAX);
    int hi = RNG(0, MAX);
    if (lo > hi) swap(lo, hi);
    ++hi;
    vc<int> B = {A.begin() + L, A.begin() + R};
    vc<int> Y = {X.begin() + L, X.begin() + R};
    int t = RNG(0, 7);
    if (t == 0) { // count
      int cnt = 0;
      for (auto&& x: B)
        if (lo <= x && x < hi) cnt += 1;
      assert(WM.count(L, R, lo, hi) == cnt);
    }
    if (t == 1) { // sm
      int sm = Mono::unit();
      FOR(i, L, R) if (lo <= A[i] && A[i] < hi) sm = Mono::op(sm, X[i]);
      assert(WM.prod(L, R, lo, hi) == sm);
    }
    if (t == 2) { // kth
      if (L == R) continue;
      int k = RNG(R - L);
      sort(all(B));
      assert(WM.kth(L, R, k) == B[k]);
    }
    if (is_same_v<Mono, Monoid_Add<int>> && t == 3) { // max_right
      int a = RNG(0, 10);
      int b = RNG(0, 10);
      int c = RNG(0, a * (R - L) + b * MAX * (R - L) + 1);
      auto check = [&](int cut, int cnt, int sm) -> bool { return a * cnt + b * sm <= c; };
      auto p = WM.max_right(check, L, R);
      int cnt = 0, sm = 0;
      binary_search(
          [&](int y) -> bool {
            auto [c, s] = WM.prefix_count_and_prod(L, R, y);
            if (check(0, c, s)) cnt = c, sm = s;
            return check(0, c, s);
          },
          -10, MAX + 10);
      assert(get<1>(p) == cnt && get<2>(p) == sm);
    }
    if (t == 4) { // k-th value and prod
      int k = RNG(0, R - L + 1);
      B.eb(infty<int>);
      auto I = argsort(B);
      int val = B[I[k]];
      int sm = Mono::unit();
      FOR(i, k) sm = Mono::op(sm, Y[I[i]]);
      auto p = WM.kth_value_and_prod(L, R, k);
      assert(p.fi == val && p.se == sm);
    }
    if (t == 5) { // next
      int x = RNG(-1, MAX + 2);
      int ans = infty<int>;
      for (auto& b: B) {
        if (x <= b) chmin(ans, b);
      }
      assert(ans == WM.next(L, R, x));
    }
    if (t == 6) { // prev
      int x = RNG(-1, MAX + 1);
      int ans = -infty<int>;
      for (auto& b: B) {
        if (b <= x) chmax(ans, b);
      }
      assert(ans == WM.prev(L, R, x));
    }
  }
}

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

signed main() {
  FOR(N, 64) {
    FOR(50) {
      test<true, Static_Range_Product_Group<Monoid_Add<int>>>(N);
      test<false, Static_Range_Product_Group<Monoid_Add<int>>>(N);
      test<true, SegTree<Monoid_Min<int>>>(N);
      test<false, SegTree<Monoid_Min<int>>>(N);
    }
  }
  solve();

  return 0;
}
#line 1 "test/1_mytest/wavelet_matrix.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
// https://codeforces.com/blog/entry/126772?#comment-1154880
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#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_max = priority_queue<T>;
template <class T>
using pq_min = 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 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_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (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 kth_bit(int k) {
  return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
  return x >> k & 1;
}

template <typename UINT>
struct all_bit {
  struct iter {
    UINT s;
    iter(UINT s) : s(s) {}
    int operator*() const { return lowbit(s); }
    iter &operator++() {
      s &= s - 1;
      return *this;
    }
    bool operator!=(const iter) const { return s != 0; }
  };
  UINT s;
  all_bit(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename UINT>
struct all_subset {
  static_assert(is_unsigned<UINT>::value);
  struct iter {
    UINT s, t;
    bool ed;
    iter(UINT s) : s(s), t(s), ed(0) {}
    int operator*() const { return s ^ t; }
    iter &operator++() {
      (t == 0 ? ed = 1 : t = (t - 1) & s);
      return *this;
    }
    bool operator!=(const iter) const { return !ed; }
  };
  UINT s;
  all_subset(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

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 U &A) {
  return std::accumulate(A.begin(), A.end(), T{});
}

#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_min<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pq_max<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 4 "test/1_mytest/wavelet_matrix.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 1 "ds/bit_vector.hpp"
struct Bit_Vector {
  int n;
  bool prepared = 0;
  vc<pair<u64, u32>> dat;
  Bit_Vector(int n = 0) : n(n) { dat.assign((n + 127) >> 6, {0, 0}); }
  void set(int i) {
    assert(!prepared && (0 <= i && i < n));
    dat[i >> 6].fi |= u64(1) << (i & 63);
  }
  void reset() {
    fill(all(dat), pair<u64, u32>{0, 0});
    prepared = 0;
  }
  void build() {
    prepared = 1;
    FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
  }
  // [0, k) 内の 1 の個数
  bool operator[](int i) { return dat[i >> 6].fi >> (i & 63) & 1; }
  int count_prefix(int k, bool f = true) {
    assert(prepared);
    auto [a, b] = dat[k >> 6];
    int ret = b + popcnt(a & ((u64(1) << (k & 63)) - 1));
    return (f ? ret : k - ret);
  }
  int count(int L, int R, bool f = true) { return count_prefix(R, f) - count_prefix(L, f); }
  string to_string() {
    string ans;
    FOR(i, n) ans += '0' + (dat[i / 64].fi >> (i % 64) & 1);
    return ans;
  }
};
#line 1 "ds/index_compression.hpp"
template <typename T>
struct Index_Compression_DISTINCT_SMALL {
  static_assert(is_same_v<T, int>);
  int mi, ma;
  vc<int> dat;
  vc<int> build(vc<int> X) {
    mi = 0, ma = -1;
    if (!X.empty()) mi = MIN(X), ma = MAX(X);
    dat.assign(ma - mi + 2, 0);
    for (auto& x: X) dat[x - mi + 1]++;
    FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
    for (auto& x: X) { x = dat[x - mi]++; }
    FOR_R(i, 1, len(dat)) dat[i] = dat[i - 1];
    dat[0] = 0;
    return X;
  }
  int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};

template <typename T>
struct Index_Compression_SAME_SMALL {
  static_assert(is_same_v<T, int>);
  int mi, ma;
  vc<int> dat;
  vc<int> build(vc<int> X) {
    mi = 0, ma = -1;
    if (!X.empty()) mi = MIN(X), ma = MAX(X);
    dat.assign(ma - mi + 2, 0);
    for (auto& x: X) dat[x - mi + 1] = 1;
    FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
    for (auto& x: X) { x = dat[x - mi]; }
    return X;
  }
  int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};

template <typename T>
struct Index_Compression_SAME_LARGE {
  vc<T> dat;
  vc<int> build(vc<T> X) {
    vc<int> I = argsort(X);
    vc<int> res(len(X));
    for (auto& i: I) {
      if (!dat.empty() && dat.back() == X[i]) {
        res[i] = len(dat) - 1;
      } else {
        res[i] = len(dat);
        dat.eb(X[i]);
      }
    }
    dat.shrink_to_fit();
    return res;
  }
  int operator()(T x) { return LB(dat, x); }
};

template <typename T>
struct Index_Compression_DISTINCT_LARGE {
  vc<T> dat;
  vc<int> build(vc<T> X) {
    vc<int> I = argsort(X);
    vc<int> res(len(X));
    for (auto& i: I) { res[i] = len(dat), dat.eb(X[i]); }
    dat.shrink_to_fit();
    return res;
  }
  int operator()(T x) { return LB(dat, x); }
};

template <typename T, bool SMALL>
using Index_Compression_DISTINCT = typename std::conditional<SMALL, Index_Compression_DISTINCT_SMALL<T>, Index_Compression_DISTINCT_LARGE<T>>::type;
template <typename T, bool SMALL>
using Index_Compression_SAME = typename std::conditional<SMALL, Index_Compression_SAME_SMALL<T>, Index_Compression_SAME_LARGE<T>>::type;

// SAME: [2,3,2] -> [0,1,0]
// DISTINCT: [2,2,3] -> [0,2,1]
// build で列を圧縮してくれる. そのあと
// (x): lower_bound(X,x) をかえす
template <typename T, bool SAME, bool SMALL>
using Index_Compression = typename std::conditional<SAME, Index_Compression_SAME<T, SMALL>, Index_Compression_DISTINCT<T, SMALL>>::type;
#line 2 "alg/monoid/add.hpp"

template <typename E>
struct Monoid_Add {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
  static constexpr X inverse(const X &x) noexcept { return -x; }
  static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
  static constexpr X unit() { return X(0); }
  static constexpr bool commute = true;
};
#line 4 "ds/wavelet_matrix/wavelet_matrix.hpp"

// 静的メソッドinverseの存在をチェックするテンプレート

template <typename, typename = std::void_t<>>
struct has_inverse : std::false_type {};

template <typename T>
struct has_inverse<T, std::void_t<decltype(T::inverse(std::declval<typename T::value_type>()))>> : std::true_type {};

struct Dummy_Data_Structure {
  using MX = Monoid_Add<bool>;
  void build(const vc<bool>& A) {}
};

template <typename Y, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix {
  using Mono = typename SEGTREE::MX;
  using T = typename Mono::value_type;
  static_assert(Mono::commute);

  int n, log, K;
  Index_Compression<Y, true, SMALL_Y> IDX;
  vc<Y> ItoY;
  vc<int> mid;
  vc<Bit_Vector> bv;
  vc<SEGTREE> seg;

  Wavelet_Matrix() {}
  Wavelet_Matrix(const vc<Y>& A) { build(A); }
  Wavelet_Matrix(const vc<Y>& A, vc<T>& SUM_Data) { build(A, SUM_Data); }
  template <typename F>
  Wavelet_Matrix(int n, F f) {
    build(n, f);
  }

  template <typename F>
  void build(int m, F f) {
    vc<Y> A(m);
    vc<T> S(m);
    for (int i = 0; i < m; ++i) {
      auto p = f(i);
      A[i] = p.fi, S[i] = p.se;
    }
    build(A, S);
  }

  void build(const vc<Y>& A) { build(A, vc<T>(len(A), Mono::unit())); }
  void build(const vc<Y>& A, vc<T> S) {
    n = len(A);
    vc<int> B = IDX.build(A);
    K = 0;
    for (auto& x: B) chmax(K, x + 1);
    ItoY.resize(K);
    FOR(i, n) ItoY[B[i]] = A[i];
    log = 0;
    while ((1 << log) < K) ++log;
    mid.resize(log), bv.assign(log, Bit_Vector(n));
    vc<int> B0(n), B1(n);
    vc<T> S0(n), S1(n);
    seg.resize(log + 1);
    seg[log].build(S);
    for (int d = log - 1; d >= 0; --d) {
      int p0 = 0, p1 = 0;
      for (int i = 0; i < n; ++i) {
        bool f = (B[i] >> d & 1);
        if (!f) { B0[p0] = B[i], S0[p0] = S[i], p0++; }
        if (f) { bv[d].set(i), B1[p1] = B[i], S1[p1] = S[i], p1++; }
      }
      swap(B, B0), swap(S, S0);
      move(B1.begin(), B1.begin() + p1, B.begin() + p0);
      move(S1.begin(), S1.begin() + p1, S.begin() + p0);
      mid[d] = p0, bv[d].build(), seg[d].build(S);
    }
  }

  // [L,R) x [0,y)

  int prefix_count(int L, int R, Y y) {
    int p = IDX(y);
    if (L == R || p == 0) return 0;
    if (p == K) return R - L;
    int cnt = 0;
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (p >> d & 1) cnt += r0 - l0, L = l1, R = r1;
      if (!(p >> d & 1)) L = l0, R = r0;
    }
    return cnt;
  }

  // [L,R) x [y1,y2)

  int count(int L, int R, Y y1, Y y2) { return prefix_count(L, R, y2) - prefix_count(L, R, y1); }

  // [L,R) x [0,y)

  pair<int, T> prefix_count_and_prod(int L, int R, Y y) {
    int p = IDX(y);
    if (p == 0) return {0, Mono::unit()};
    if (p == K) return {R - L, seg[log].prod(L, R)};
    int cnt = 0;
    T t = Mono::unit();
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (p >> d & 1) { cnt += r0 - l0, t = Mono::op(t, seg[d].prod(l0, r0)), L = l1, R = r1; }
      if (!(p >> d & 1)) L = l0, R = r0;
    }
    return {cnt, t};
  }

  // [L,R) x [y1,y2)

  pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) {
    if constexpr (has_inverse<Mono>::value) {
      auto [c1, t1] = prefix_count_and_prod(L, R, y1);
      auto [c2, t2] = prefix_count_and_prod(L, R, y2);
      return {c2 - c1, Mono::op(Mono::inverse(t1), t2)};
    }
    int lo = IDX(y1), hi = IDX(y2), cnt = 0;
    T t = Mono::unit();
    auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
      assert(b - a == (1 << d));
      if (hi <= a || b <= lo) return;
      if (lo <= a && b <= hi) {
        cnt += R - L, t = Mono::op(t, seg[d].prod(L, R));
        return;
      }
      --d;
      int c = (a + b) / 2;
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
    };
    dfs(dfs, log, L, R, 0, 1 << log);
    return {cnt, t};
  }

  // [L,R) x [y1,y2)

  T prefix_prod(int L, int R, Y y) { return prefix_count_and_prod(L, R, y).se; }
  // [L,R) x [y1,y2)

  T prod(int L, int R, Y y1, Y y2) { return count_and_prod(L, R, y1, y2).se; }
  T prod_all(int L, int R) { return seg[log].prod(L, R); }

  Y kth(int L, int R, int k) {
    assert(0 <= k && k < R - L);
    int p = 0;
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (k < r0 - l0) {
        L = l0, R = r0;
      } else {
        k -= r0 - l0, L = l1, R = r1, p |= 1 << d;
      }
    }
    return ItoY[p];
  }

  // y 以上最小 OR infty<Y>

  Y next(int L, int R, Y y) {
    int k = IDX(y);
    int p = K;

    auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
      if (p <= a || L == R || b <= k) return;
      if (d == 0) {
        chmin(p, a);
        return;
      }
      --d;
      int c = (a + b) / 2;
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
    };
    dfs(dfs, log, L, R, 0, 1 << log);
    return (p == K ? infty<Y> : ItoY[p]);
  }

  // y 以下最大 OR -infty<T>

  Y prev(int L, int R, Y y) {
    int k = IDX(y + 1);
    int p = -1;
    auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
      if (b - 1 <= p || L == R || k <= a) return;
      if (d == 0) {
        chmax(p, a);
        return;
      }
      --d;
      int c = (a + b) / 2;
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      dfs(dfs, d, l1, r1, c, b), dfs(dfs, d, l0, r0, a, c);
    };
    dfs(dfs, log, L, R, 0, 1 << log);
    return (p == -1 ? -infty<Y> : ItoY[p]);
  }

  Y median(bool UPPER, int L, int R) {
    assert(0 <= L && L < R && R <= n);
    int k = (UPPER ? (R - L) / 2 : (R - L - 1) / 2);
    return kth(L, R, k);
  }

  pair<Y, T> kth_value_and_prod(int L, int R, int k) {
    assert(0 <= k && k <= R - L);
    if (k == R - L) return {infty<Y>, seg[log].prod(L, R)};
    int p = 0;
    T t = Mono::unit();
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (k < r0 - l0) {
        L = l0, R = r0;
      } else {
        t = Mono::op(t, seg[d].prod(l0, r0)), k -= r0 - l0, L = l1, R = r1, p |= 1 << d;
      }
    }
    t = Mono::op(t, seg[0].prod(L, L + k));
    return {ItoY[p], t};
  }

  T prod_index_range(int L, int R, int k1, int k2) {
    static_assert(has_inverse<Mono>::value);
    T t1 = kth_value_and_prod(L, R, k1).se;
    T t2 = kth_value_and_prod(L, R, k2).se;
    return Mono::op(Mono::inverse(t1), t2);
  }

  // [L,R) x [0,y) での check(y, cnt, prod) が true となる最大の (cnt,prod)

  // ただし y はぴったりのところだけです

  template <typename F>
  tuple<Y, int, T> max_right(F check, int L, int R) {
    int cnt = 0;
    int p = 0;
    T t = Mono::unit();
    assert(check(-infty<Y>, 0, Mono::unit()));
    if (check(infty<Y>, R - L, seg[log].prod(L, R))) { return {infty<Y>, R - L, seg[log].prod(L, R)}; }
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      int cnt1 = cnt + r0 - l0;
      int p1 = p | 1 << d;
      T t1 = Mono::op(t, seg[d].prod(l0, r0));
      int y1 = (p1 < len(ItoY) ? ItoY[p1] : infty<Y>);
      if (check(y1, cnt1, t1)) {
        p = p1, cnt = cnt1, t = t1, L = l1, R = r1;
      } else {
        L = l0, R = r0;
      }
    }
    int y = (p < len(ItoY) ? ItoY[p] : infty<Y>);
    return {y, cnt, t};
  }

  void set(int i, T t) {
    assert(0 <= i && i < n);
    int L = i, R = i + 1;
    seg[log].set(L, t);
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (l0 < r0) L = l0, R = r0;
      if (l0 == r0) L = l1, R = r1;
      seg[d].set(L, t);
    }
  }
  void multiply(int i, T t) {
    assert(0 <= i && i < n);
    int L = i, R = i + 1;
    seg[log].multiply(L, t);
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (l0 < r0) L = l0, R = r0;
      if (l0 == r0) L = l1, R = r1;
      seg[d].multiply(L, t);
    }
  }
  void add(int i, T t) { multiply(i, t); }
};
#line 2 "ds/static_range_product_group.hpp"

template <typename Monoid>
struct Static_Range_Product_Group {
  using MX = Monoid;
  using X = typename MX::value_type;
  int n;
  vc<X> dat;
  Static_Range_Product_Group() {}
  template <typename F>
  Static_Range_Product_Group(int m, F f) {
    build(m, f);
  }
  Static_Range_Product_Group(vc<X>& A) {
    build(len(A), [&](int i) -> X { return A[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m;
    dat.assign(n + 1, MX::unit());
    for (int i = 0; i < n; ++i) dat[i + 1] = MX::op(dat[i], f(i));
  }
  void build(vc<X>& A) {
    n = len(A);
    dat.assign(n + 1, MX::unit());
    for (int i = 0; i < n; ++i) dat[i + 1] = MX::op(dat[i], A[i]);
  }
  X prod(int l, int r) { return MX::op(MX::inverse(dat[l]), dat[r]); }
};

template <typename T>
using Prefix_Sum = Static_Range_Product_Group<Monoid_Add<T>>;
#line 2 "ds/segtree/segtree.hpp"

template <class Monoid>
struct SegTree {
  using MX = Monoid;
  using X = typename MX::value_type;
  using value_type = X;
  vc<X> dat;
  int n, log, size;

  SegTree() {}
  SegTree(int n) { build(n); }
  template <typename F>
  SegTree(int n, F f) {
    build(n, f);
  }
  SegTree(const vc<X>& v) { build(v); }

  void build(int m) {
    build(m, [](int i) -> X { return MX::unit(); });
  }
  void build(const vc<X>& v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m, log = 1;
    while ((1 << log) < n) ++log;
    size = 1 << log;
    dat.assign(size << 1, MX::unit());
    FOR(i, n) dat[size + i] = f(i);
    FOR_R(i, 1, size) update(i);
  }

  X get(int i) { return dat[size + i]; }
  vc<X> get_all() { return {dat.begin() + size, dat.begin() + size + n}; }

  void update(int i) { dat[i] = Monoid::op(dat[2 * i], dat[2 * i + 1]); }
  void set(int i, const X& x) {
    assert(i < n);
    dat[i += size] = x;
    while (i >>= 1) update(i);
  }

  void multiply(int i, const X& x) {
    assert(i < n);
    i += size;
    dat[i] = Monoid::op(dat[i], x);
    while (i >>= 1) update(i);
  }

  X prod(int L, int R) {
    assert(0 <= L && L <= R && R <= n);
    X vl = Monoid::unit(), vr = Monoid::unit();
    L += size, R += size;
    while (L < R) {
      if (L & 1) vl = Monoid::op(vl, dat[L++]);
      if (R & 1) vr = Monoid::op(dat[--R], vr);
      L >>= 1, R >>= 1;
    }
    return Monoid::op(vl, vr);
  }

  X prod_all() { return dat[1]; }

  template <class F>
  int max_right(F check, int L) {
    assert(0 <= L && L <= n && check(Monoid::unit()));
    if (L == n) return n;
    L += size;
    X sm = Monoid::unit();
    do {
      while (L % 2 == 0) L >>= 1;
      if (!check(Monoid::op(sm, dat[L]))) {
        while (L < size) {
          L = 2 * L;
          if (check(Monoid::op(sm, dat[L]))) { sm = Monoid::op(sm, dat[L++]); }
        }
        return L - size;
      }
      sm = Monoid::op(sm, dat[L++]);
    } while ((L & -L) != L);
    return n;
  }

  template <class F>
  int min_left(F check, int R) {
    assert(0 <= R && R <= n && check(Monoid::unit()));
    if (R == 0) return 0;
    R += size;
    X sm = Monoid::unit();
    do {
      --R;
      while (R > 1 && (R % 2)) R >>= 1;
      if (!check(Monoid::op(dat[R], sm))) {
        while (R < size) {
          R = 2 * R + 1;
          if (check(Monoid::op(dat[R], sm))) { sm = Monoid::op(dat[R--], sm); }
        }
        return R + 1 - size;
      }
      sm = Monoid::op(dat[R], sm);
    } while ((R & -R) != R);
    return 0;
  }

  // prod_{l<=i<r} A[i xor x]
  X xor_prod(int l, int r, int xor_val) {
    static_assert(Monoid::commute);
    X x = Monoid::unit();
    for (int k = 0; k < log + 1; ++k) {
      if (l >= r) break;
      if (l & 1) { x = Monoid::op(x, dat[(size >> k) + ((l++) ^ xor_val)]); }
      if (r & 1) { x = Monoid::op(x, dat[(size >> k) + ((--r) ^ xor_val)]); }
      l /= 2, r /= 2, xor_val /= 2;
    }
    return x;
  }
};
#line 2 "alg/monoid/min.hpp"

template <typename E>
struct Monoid_Min {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return min(x, y); }
  static constexpr X unit() { return infty<E>; }
  static constexpr bool commute = true;
};
#line 10 "test/1_mytest/wavelet_matrix.test.cpp"

template <bool SMALL_Y, typename SEGTREE>
void test(int N) {
  int MAX = RNG(2, 1 << 10);
  vc<int> A(N);
  vc<int> X(N);
  FOR(i, N) X[i] = RNG(MAX);
  FOR(i, N) A[i] = RNG(MAX);

  Wavelet_Matrix<int, false, SEGTREE> WM(A, X);
  using Mono = typename SEGTREE::MX;

  int Q = 100;
  FOR(Q) {
    int L = RNG(0, max(1, N));
    int R = RNG(0, max(1, N + 1));
    if (L > R) swap(L, R);
    int lo = RNG(0, MAX);
    int hi = RNG(0, MAX);
    if (lo > hi) swap(lo, hi);
    ++hi;
    vc<int> B = {A.begin() + L, A.begin() + R};
    vc<int> Y = {X.begin() + L, X.begin() + R};
    int t = RNG(0, 7);
    if (t == 0) { // count
      int cnt = 0;
      for (auto&& x: B)
        if (lo <= x && x < hi) cnt += 1;
      assert(WM.count(L, R, lo, hi) == cnt);
    }
    if (t == 1) { // sm
      int sm = Mono::unit();
      FOR(i, L, R) if (lo <= A[i] && A[i] < hi) sm = Mono::op(sm, X[i]);
      assert(WM.prod(L, R, lo, hi) == sm);
    }
    if (t == 2) { // kth
      if (L == R) continue;
      int k = RNG(R - L);
      sort(all(B));
      assert(WM.kth(L, R, k) == B[k]);
    }
    if (is_same_v<Mono, Monoid_Add<int>> && t == 3) { // max_right
      int a = RNG(0, 10);
      int b = RNG(0, 10);
      int c = RNG(0, a * (R - L) + b * MAX * (R - L) + 1);
      auto check = [&](int cut, int cnt, int sm) -> bool { return a * cnt + b * sm <= c; };
      auto p = WM.max_right(check, L, R);
      int cnt = 0, sm = 0;
      binary_search(
          [&](int y) -> bool {
            auto [c, s] = WM.prefix_count_and_prod(L, R, y);
            if (check(0, c, s)) cnt = c, sm = s;
            return check(0, c, s);
          },
          -10, MAX + 10);
      assert(get<1>(p) == cnt && get<2>(p) == sm);
    }
    if (t == 4) { // k-th value and prod
      int k = RNG(0, R - L + 1);
      B.eb(infty<int>);
      auto I = argsort(B);
      int val = B[I[k]];
      int sm = Mono::unit();
      FOR(i, k) sm = Mono::op(sm, Y[I[i]]);
      auto p = WM.kth_value_and_prod(L, R, k);
      assert(p.fi == val && p.se == sm);
    }
    if (t == 5) { // next
      int x = RNG(-1, MAX + 2);
      int ans = infty<int>;
      for (auto& b: B) {
        if (x <= b) chmin(ans, b);
      }
      assert(ans == WM.next(L, R, x));
    }
    if (t == 6) { // prev
      int x = RNG(-1, MAX + 1);
      int ans = -infty<int>;
      for (auto& b: B) {
        if (b <= x) chmax(ans, b);
      }
      assert(ans == WM.prev(L, R, x));
    }
  }
}

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

signed main() {
  FOR(N, 64) {
    FOR(50) {
      test<true, Static_Range_Product_Group<Monoid_Add<int>>>(N);
      test<false, Static_Range_Product_Group<Monoid_Add<int>>>(N);
      test<true, SegTree<Monoid_Min<int>>>(N);
      test<false, SegTree<Monoid_Min<int>>>(N);
    }
  }
  solve();

  return 0;
}
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