test/1_mytest/prefix_max_segtree.test.cpp

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• Last update: 2025-01-27 19:24:29+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• alg/monoid/affine.hpp
• ds/segtree/prefix_max_segtree.hpp
• mod/modint.hpp
• mod/modint_common.hpp
• my_template.hpp
• random/base.hpp

Code

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

#include "my_template.hpp"

#include "ds/segtree/prefix_max_segtree.hpp"
#include "random/base.hpp"
#include "alg/monoid/affine.hpp"
#include "mod/modint.hpp"

using mint = modint998;
using F = pair<mint, mint>;

void test(ll N) {
  vc<int> key(N);
  vc<F> X(N);
  auto get = [&]() -> pair<int, F> {
    int k = RNG(0, 100);
    mint a = RNG(0, mint::get_mod());
    mint b = RNG(0, mint::get_mod());
    return {k, {a, b}};
  };

  FOR(i, N) tie(key[i], X[i]) = get();

  auto segf = [&](int i) -> pair<int, F> { return {key[i], X[i]}; };

  using Mono = Monoid_Affine<mint>;
  Prefix_Max_SegTree<int, Mono> seg(N, segf);

  auto naive = [&](int L, int R) -> F {
    int mx = -infty<int>;
    F prod = Mono::unit();
    FOR(i, L, R) {
      if (mx <= key[i]) {
        mx = key[i];
        prod = Mono::op(prod, X[i]);
      }
    }
    return prod;
  };

  /*
  set
  get
  get_all
  prod
  prod_all
  */
  int Q = 1000;
  FOR(Q) {
    int t = RNG(0, 5);
    int i = RNG(0, N);
    int L = RNG(0, N), R = RNG(0, N);
    auto [k, x] = get();
    if (L > R) swap(L, R);
    ++R;
    if (t == 0) {
      key[i] = k, X[i] = x;
      seg.set(i, {k, x});
    }
    if (t == 1) {
      auto [k, x] = seg.get(i);
      assert(key[i] == k);
      assert(X[i] == x);
    }
    if (t == 2) {
      auto [k, x] = seg.get_all();
      assert(key == k);
      assert(X == x);
    }
    if (t == 3) { assert(naive(L, R) == seg.prod(L, R)); }
    if (t == 4) { assert(naive(0, N) == seg.prod_all()); }
  }
}

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

signed main() {
  FOR(100) FOR(N, 1, 100) { test(N); }
  solve();
  return 0;
}

#line 1 "test/1_mytest/prefix_max_segtree.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 = 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 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 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 4 "test/1_mytest/prefix_max_segtree.test.cpp"

#line 1 "ds/segtree/prefix_max_segtree.hpp"

/*
key[0],...,key[n-1] がある
モノイドの列 x[0],...,x[n-1] がある
query(l,r): l から見えるところに対する monoid product
見える: key[i]==max(key[0]...key[i])
Qlog^2n
https://qoj.ac/contest/1540/problem/8338
*/
template <typename KEY_TYPE, typename Monoid>
struct Prefix_Max_SegTree {
  using MX = Monoid;
  using KEY = KEY_TYPE;
  using X = typename MX::value_type;
  int n, size, log;
  struct Data {
    KEY max;
    X prod, rprod; // rprod はこの区間だけで計算したときの右側
  };

  vc<Data> dat;

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

  void build(int m) {
    build(m, [](int i) -> pair<KEY, X> { return {-infty<int>, MX::unit()}; });
  }
  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, {-infty<int>, MX::unit(), MX::unit()});
    FOR(i, n) {
      auto [k, x] = f(i);
      dat[size + i] = {k, x, MX::unit()};
    }
    FOR_R(i, 1, size) update(i);
  }

  void set(int i, pair<KEY, X> p) {
    int k = p.fi;
    X x = p.se;
    i += size;
    dat[i] = {k, x, MX::unit()};
    while (i > 1) i /= 2, update(i);
  }

  X prod_all() { return dat[1].prod; }
  X prod(int L, int R) {
    KEY k = -infty<KEY>;
    vc<int> suff;
    L += size, R += size;
    X prod = MX::unit();
    while (L < R) {
      if (L & 1) { prod = MX::op(prod, dfs(L, k)), chmax(k, dat[L].max), ++L; }
      if (R & 1) { suff.eb(--R); }
      L /= 2, R /= 2;
    }
    reverse(all(suff));
    for (auto& v: suff) { prod = MX::op(prod, dfs(v, k)), chmax(k, dat[v].max); }
    return prod;
  }

  pair<KEY, X> get(int i) { return {dat[size + i].max, dat[size + i].prod}; }
  pair<vc<KEY>, vc<X>> get_all() {
    vc<KEY> key(n);
    vc<X> x(n);
    FOR(i, n) key[i] = dat[size + i].max, x[i] = dat[size + i].prod;
    return {key, x};
  }

private:
  void update(int i) {
    assert(0 <= i && i < size);
    dat[i].max = max(dat[2 * i + 0].max, dat[2 * i + 1].max);
    dat[i].rprod = dfs(2 * i + 1, dat[2 * i + 0].max);
    dat[i].prod = MX::op(dat[2 * i + 0].prod, dat[i].rprod);
  }

  X dfs(int v, KEY k) {
    // prefix に k を置いた場合の subtree(v) での値
    if (size <= v) { return (k <= dat[v].max ? dat[v].prod : MX::unit()); }
    if (k <= dat[2 * v + 0].max) { return MX::op(dfs(2 * v + 0, k), dat[v].rprod); }
    return dfs(2 * v + 1, k);
  }
};
#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 "alg/monoid/affine.hpp"

// op(F, G) = comp(G,F), F のあとで G
template <typename K>
struct Monoid_Affine {
  using F = pair<K, K>;
  using value_type = F;
  using X = value_type;
  static constexpr F op(const F &x, const F &y) noexcept {
    return F({x.first * y.first, x.second * y.first + y.second});
  }
  static constexpr F inverse(const F &x) {
    auto [a, b] = x;
    a = K(1) / a;
    return {a, a * (-b)};
  }
  static constexpr K eval(const F &f, K x) noexcept {
    return f.first * x + f.second;
  }
  static constexpr F unit() { return {K(1), K(0)}; }
  static constexpr bool commute = false;
};
#line 2 "mod/modint_common.hpp"

struct has_mod_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};

template <typename mint>
mint inv(int n) {
  static const int mod = mint::get_mod();
  static vector<mint> dat = {0, 1};
  assert(0 <= n);
  if (n >= mod) n %= mod;
  while (len(dat) <= n) {
    int k = len(dat);
    int q = (mod + k - 1) / k;
    dat.eb(dat[k * q - mod] * mint::raw(q));
  }
  return dat[n];
}

template <typename mint>
mint fact(int n) {
  static const int mod = mint::get_mod();
  assert(0 <= n && n < mod);
  static vector<mint> dat = {1, 1};
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
  return dat[n];
}

template <typename mint>
mint fact_inv(int n) {
  static vector<mint> dat = {1, 1};
  if (n < 0) return mint(0);
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
  return dat[n];
}

template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
  return (mint(1) * ... * fact_inv<mint>(xs));
}

template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
  return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}

template <typename mint>
mint C_dense(int n, int k) {
  assert(n >= 0);
  if (k < 0 || n < k) return 0;
  static vvc<mint> C;
  static int H = 0, W = 0;
  auto calc = [&](int i, int j) -> mint {
    if (i == 0) return (j == 0 ? mint(1) : mint(0));
    return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
  };
  if (W <= k) {
    FOR(i, H) {
      C[i].resize(k + 1);
      FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
    }
    W = k + 1;
  }
  if (H <= n) {
    C.resize(n + 1);
    FOR(i, H, n + 1) {
      C[i].resize(W);
      FOR(j, W) { C[i][j] = calc(i, j); }
    }
    H = n + 1;
  }
  return C[n][k];
}

template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
  assert(n >= 0);
  if (k < 0 || n < k) return 0;
  if constexpr (dense) return C_dense<mint>(n, k);
  if constexpr (!large) return multinomial<mint>(n, k, n - k);
  k = min(k, n - k);
  mint x(1);
  FOR(i, k) x *= mint(n - i);
  return x * fact_inv<mint>(k);
}

template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
  assert(n >= 0);
  assert(0 <= k && k <= n);
  if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
  return mint(1) / C<mint, 1>(n, k);
}

// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
  assert(n >= 0);
  if (d < 0) return mint(0);
  if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
  return C<mint, large, dense>(n + d - 1, d);
}
#line 3 "mod/modint.hpp"

template <int mod>
struct modint {
  static constexpr u32 umod = u32(mod);
  static_assert(umod < u32(1) << 31);
  u32 val;

  static modint raw(u32 v) {
    modint x;
    x.val = v;
    return x;
  }
  constexpr modint() : val(0) {}
  constexpr modint(u32 x) : val(x % umod) {}
  constexpr modint(u64 x) : val(x % umod) {}
  constexpr modint(u128 x) : val(x % umod) {}
  constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
  bool operator<(const modint &other) const { return val < other.val; }
  modint &operator+=(const modint &p) {
    if ((val += p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator-=(const modint &p) {
    if ((val += umod - p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator*=(const modint &p) {
    val = u64(val) * p.val % umod;
    return *this;
  }
  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }
  modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
  modint operator+(const modint &p) const { return modint(*this) += p; }
  modint operator-(const modint &p) const { return modint(*this) -= p; }
  modint operator*(const modint &p) const { return modint(*this) *= p; }
  modint operator/(const modint &p) const { return modint(*this) /= p; }
  bool operator==(const modint &p) const { return val == p.val; }
  bool operator!=(const modint &p) const { return val != p.val; }
  modint inverse() const {
    int a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint(u);
  }
  modint pow(ll n) const {
    assert(n >= 0);
    modint ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  static constexpr int get_mod() { return mod; }
  // (n, r), r は 1 の 2^n 乗根
  static constexpr pair<int, int> ntt_info() {
    if (mod == 120586241) return {20, 74066978};
    if (mod == 167772161) return {25, 17};
    if (mod == 469762049) return {26, 30};
    if (mod == 754974721) return {24, 362};
    if (mod == 880803841) return {23, 211};
    if (mod == 943718401) return {22, 663003469};
    if (mod == 998244353) return {23, 31};
    if (mod == 1004535809) return {21, 582313106};
    if (mod == 1012924417) return {21, 368093570};
    return {-1, -1};
  }
  static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};

#ifdef FASTIO
template <int mod>
void rd(modint<mod> &x) {
  fastio::rd(x.val);
  x.val %= mod;
  // assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
  fastio::wt(x.val);
}
#endif

using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 9 "test/1_mytest/prefix_max_segtree.test.cpp"

using mint = modint998;
using F = pair<mint, mint>;

void test(ll N) {
  vc<int> key(N);
  vc<F> X(N);
  auto get = [&]() -> pair<int, F> {
    int k = RNG(0, 100);
    mint a = RNG(0, mint::get_mod());
    mint b = RNG(0, mint::get_mod());
    return {k, {a, b}};
  };

  FOR(i, N) tie(key[i], X[i]) = get();

  auto segf = [&](int i) -> pair<int, F> { return {key[i], X[i]}; };

  using Mono = Monoid_Affine<mint>;
  Prefix_Max_SegTree<int, Mono> seg(N, segf);

  auto naive = [&](int L, int R) -> F {
    int mx = -infty<int>;
    F prod = Mono::unit();
    FOR(i, L, R) {
      if (mx <= key[i]) {
        mx = key[i];
        prod = Mono::op(prod, X[i]);
      }
    }
    return prod;
  };

  /*
  set
  get
  get_all
  prod
  prod_all
  */
  int Q = 1000;
  FOR(Q) {
    int t = RNG(0, 5);
    int i = RNG(0, N);
    int L = RNG(0, N), R = RNG(0, N);
    auto [k, x] = get();
    if (L > R) swap(L, R);
    ++R;
    if (t == 0) {
      key[i] = k, X[i] = x;
      seg.set(i, {k, x});
    }
    if (t == 1) {
      auto [k, x] = seg.get(i);
      assert(key[i] == k);
      assert(X[i] == x);
    }
    if (t == 2) {
      auto [k, x] = seg.get_all();
      assert(key == k);
      assert(X == x);
    }
    if (t == 3) { assert(naive(L, R) == seg.prod(L, R)); }
    if (t == 4) { assert(naive(0, N) == seg.prod_all()); }
  }
}

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

signed main() {
  FOR(100) FOR(N, 1, 100) { test(N); }
  solve();
  return 0;
}

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