test/1_mytest/blackbox_solve_linear.test.cpp

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• Last update: 2024-12-26 06:32:57+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• linalg/blackbox/solve_linear.hpp
• linalg/det.hpp
• linalg/matrix_mul.hpp
• mod/barrett.hpp
• mod/modint.hpp
• mod/modint_common.hpp
• my_template.hpp
• random/base.hpp
• random/random_matrix.hpp

Code

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

#include "my_template.hpp"

#include "random/random_matrix.hpp"
#include "linalg/blackbox/solve_linear.hpp"

using mint = modint998;

void test() {
  FOR(100) {
    FOR(N, 1, 10) FOR(M, 1, 10) FOR(R, 0, 10) {
      if (R > N || R > M) continue;
      vvc<mint> A = random_matrix<mint>(N, M, R);
      vc<tuple<int, int, mint>> mat;
      FOR(i, N) FOR(j, M) mat.eb(i, j, A[i][j]);
      vc<mint> x(N), y(M);
      FOR(i, M) y[i] = RNG(0, mint::get_mod());
      FOR(i, N) FOR(j, M) x[i] += A[i][j] * y[j];
      if (RNG(0, 2) == 0) { FOR(i, M) y[i] = RNG(0, 2); }
      int fail = 0;
      FOR(5) {
        vc<mint> ans = sparse_solve_linear<mint>(N, M, mat, x);
        if (ans.empty()) ++fail;
      }
      assert(fail <= 1);
    }
  }
}

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

signed main() {
  test();
  solve();
  return 0;
}

#line 1 "test/1_mytest/blackbox_solve_linear.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 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/blackbox_solve_linear.test.cpp"

#line 1 "random/random_matrix.hpp"

#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 "mod/barrett.hpp"

// https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp
struct Barrett {
  u32 m;
  u64 im;
  explicit Barrett(u32 m = 1) : m(m), im(u64(-1) / m + 1) {}
  u32 umod() const { return m; }
  u32 modulo(u64 z) {
    if (m == 1) return 0;
    u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
    u64 y = x * m;
    return (z - y + (z < y ? m : 0));
  }
  u64 floor(u64 z) {
    if (m == 1) return z;
    u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
    u64 y = x * m;
    return (z < y ? x - 1 : x);
  }
  pair<u64, u32> divmod(u64 z) {
    if (m == 1) return {z, 0};
    u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
    u64 y = x * m;
    if (z < y) return {x - 1, z - y + m};
    return {x, z - y};
  }
  u32 mul(u32 a, u32 b) { return modulo(u64(a) * b); }
};

struct Barrett_64 {
  u128 mod, mh, ml;

  explicit Barrett_64(u64 mod = 1) : mod(mod) {
    u128 m = u128(-1) / mod;
    if (m * mod + mod == u128(0)) ++m;
    mh = m >> 64;
    ml = m & u64(-1);
  }

  u64 umod() const { return mod; }

  u64 modulo(u128 x) {
    u128 z = (x & u64(-1)) * ml;
    z = (x & u64(-1)) * mh + (x >> 64) * ml + (z >> 64);
    z = (x >> 64) * mh + (z >> 64);
    x -= z * mod;
    return x < mod ? x : x - mod;
  }

  u64 mul(u64 a, u64 b) { return modulo(u128(a) * b); }
};
#line 2 "linalg/det.hpp"

int det_mod(vvc<int> A, int mod) {
  Barrett bt(mod);
  const int n = len(A);
  ll det = 1;
  FOR(i, n) {
    FOR(j, i, n) {
      if (A[j][i] == 0) continue;
      if (i != j) { swap(A[i], A[j]), det = mod - det; }
      break;
    }
    FOR(j, i + 1, n) {
      while (A[i][i] != 0) {
        ll c = mod - A[j][i] / A[i][i];
        FOR_R(k, i, n) { A[j][k] = bt.modulo(A[j][k] + A[i][k] * c); }
        swap(A[i], A[j]), det = mod - det;
      }
      swap(A[i], A[j]), det = mod - det;
    }
  }
  FOR(i, n) det = bt.mul(det, A[i][i]);
  return det % mod;
}

template <typename mint>
mint det(vvc<mint>& A) {
  const int n = len(A);
  vv(int, B, n, n);
  FOR(i, n) FOR(j, n) B[i][j] = A[i][j].val;
  return det_mod(B, mint::get_mod());
}
#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 3 "linalg/matrix_mul.hpp"

template <class T, typename enable_if<has_mod<T>::value>::type* = nullptr>
vc<vc<T>> matrix_mul(const vc<vc<T>>& A, const vc<vc<T>>& B, int N1 = -1,
                     int N2 = -1, int N3 = -1) {
  if (N1 == -1) { N1 = len(A), N2 = len(B), N3 = len(B[0]); }
  vv(u32, b, N3, N2);
  FOR(i, N2) FOR(j, N3) b[j][i] = B[i][j].val;
  vv(T, C, N1, N3);

  if ((T::get_mod() < (1 << 30)) && N2 <= 16) {
    FOR(i, N1) FOR(j, N3) {
      u64 sm = 0;
      FOR(m, N2) sm += u64(A[i][m].val) * b[j][m];
      C[i][j] = sm;
    }
  } else {
    FOR(i, N1) FOR(j, N3) {
      u128 sm = 0;
      FOR(m, N2) sm += u64(A[i][m].val) * b[j][m];
      C[i][j] = T::raw(sm % (T::get_mod()));
    }
  }
  return C;
}

template <class T, typename enable_if<!has_mod<T>::value>::type* = nullptr>
vc<vc<T>> matrix_mul(const vc<vc<T>>& A, const vc<vc<T>>& B, int N1 = -1,
                     int N2 = -1, int N3 = -1) {
  if (N1 == -1) { N1 = len(A), N2 = len(B), N3 = len(B[0]); }
  vv(T, b, N2, N3);
  FOR(i, N2) FOR(j, N3) b[j][i] = B[i][j];
  vv(T, C, N1, N3);
  FOR(n, N1) FOR(m, N2) FOR(k, N3) C[n][k] += A[n][m] * b[k][m];
  return C;
}

// square-matrix defined as array

template <class T, int N,
          typename enable_if<has_mod<T>::value>::type* = nullptr>
array<array<T, N>, N> matrix_mul(const array<array<T, N>, N>& A,
                                 const array<array<T, N>, N>& B) {
  array<array<T, N>, N> C{};

  if ((T::get_mod() < (1 << 30)) && N <= 16) {
    FOR(i, N) FOR(k, N) {
      u64 sm = 0;
      FOR(j, N) sm += u64(A[i][j].val) * (B[j][k].val);
      C[i][k] = sm;
    }
  } else {
    FOR(i, N) FOR(k, N) {
      u128 sm = 0;
      FOR(j, N) sm += u64(A[i][j].val) * (B[j][k].val);
      C[i][k] = sm;
    }
  }
  return C;
}

// square-matrix defined as array

template <class T, int N,
          typename enable_if<!has_mod<T>::value>::type* = nullptr>
array<array<T, N>, N> matrix_mul(const array<array<T, N>, N>& A,
                                 const array<array<T, N>, N>& B) {
  array<array<T, N>, N> C{};
  FOR(i, N) FOR(j, N) FOR(k, N) C[i][k] += A[i][j] * B[j][k];
  return C;
}
#line 5 "random/random_matrix.hpp"

template <typename mint>
vvc<mint> random_matrix(int n, int m, int rk) {
  if (n == m && m == rk) {
    while (1) {
      vv(mint, A, n, n);
      FOR(i, n) FOR(j, n) A[i][j] = RNG(0, mint::get_mod());
      if (det(A) == mint(0)) continue;
      return A;
    }
  }
  vvc<mint> L = random_matrix<mint>(n, n, n);
  vvc<mint> R = random_matrix<mint>(m, m, m);
  vv(mint, A, n, m);
  FOR(i, rk) A[i][i] = 1;
  A = matrix_mul<mint>(L, A, n, n, m);
  A = matrix_mul<mint>(A, R, n, m, m);
  return A;
}
#line 2 "linalg/blackbox/solve_linear.hpp"

// https://arxiv.org/pdf/1204.3735
template <typename mint, typename F1, typename F2>
vc<mint> blackbox_solve_linear(int N, int M, F1 apply_A, F2 apply_AT,
                               vc<mint> b) {
  assert(len(b) == N);
  vc<mint> D1(M), D2(N);
  FOR(i, M) D1[i] = RNG(0, mint::get_mod());
  FOR(i, N) D2[i] = RNG(0, mint::get_mod());
  auto apply_D1 = [&](vc<mint> &v) -> void { FOR(i, M) v[i] *= D1[i]; };
  auto apply_D2 = [&](vc<mint> &v) -> void { FOR(i, N) v[i] *= D2[i]; };
  auto apply_tilde_A = [&](vc<mint> v) -> vc<mint> {
    apply_D1(v);
    v = apply_A(v);
    apply_D2(v);
    v = apply_AT(v);
    apply_D1(v);
    return v;
  };
  vc<mint> v(M);
  FOR(i, M) v[i] = RNG(0, mint::get_mod());
  vc<mint> tilde_b = apply_tilde_A(v);
  vc<mint> c = b;
  apply_D2(c);
  c = apply_AT(c);
  apply_D1(c);
  FOR(i, M) tilde_b[i] += c[i];

  auto dot = [&](vc<mint> &a, vc<mint> &b) -> mint {
    mint ans = 0;
    FOR(i, len(a)) ans += a[i] * b[i];
    return ans;
  };
  auto is_zero = [&](vc<mint> &a) -> bool {
    FOR(i, M) if (a[i] != mint(0)) return false;
    return true;
  };

  auto solve_symmetric = [&](vc<mint> b) -> vc<mint> {
    if (is_zero(b)) return vc<mint>(M);
    vc<mint> w0(M), v0(M);
    mint t0 = 1;
    vc<mint> w1 = b, v1 = apply_tilde_A(b);
    mint t1 = dot(v1, w1);
    if (t1 == mint(0)) return {};
    vc<mint> x(M);
    mint c = dot(b, w1) / t1;
    FOR(i, M) x[i] = c * w1[i];
    while (1) {
      vc<mint> w2(M);
      mint c1 = dot(v1, v1) / t1, c0 = dot(v1, v0) / t0;
      FOR(i, M) w2[i] = v1[i] - c1 * w1[i] - c0 * w0[i];
      if (is_zero(w2)) return x;
      vc<mint> v2 = apply_tilde_A(w2);
      mint t2 = dot(w2, v2);
      if (t2 == mint(0)) return {};
      mint c = dot(b, w2) / t2;
      FOR(i, M) x[i] += c * w2[i];
      swap(v0, v1), swap(v1, v2);
      swap(w0, w1), swap(w1, w2);
      swap(t0, t1), swap(t1, t2);
    }
  };

  // tilde(A)x=tilde(b)
  vc<mint> x = solve_symmetric(tilde_b);
  if (x.empty()) return {};
  FOR(i, M) x[i] -= v[i];
  apply_D1(x);

  // check
  if (apply_A(x) != b) return {};
  return x;
}

// Ax=b
template <typename mint>
vc<mint> sparse_solve_linear(int N, int M, vc<tuple<int, int, mint>> mat,
                             vc<mint> b) {
  assert(len(b) == N);
  auto apply = [&](vc<mint> a) -> vc<mint> {
    assert(len(a) == M);
    vc<mint> b(N);
    for (auto &[i, j, x]: mat) b[i] += a[j] * x;
    return b;
  };
  auto apply_T = [&](vc<mint> a) -> vc<mint> {
    assert(len(a) == N);
    vc<mint> b(M);
    for (auto &[i, j, x]: mat) b[j] += a[i] * x;
    return b;
  };
  return blackbox_solve_linear<mint>(N, M, apply, apply_T, b);
}
#line 7 "test/1_mytest/blackbox_solve_linear.test.cpp"

using mint = modint998;

void test() {
  FOR(100) {
    FOR(N, 1, 10) FOR(M, 1, 10) FOR(R, 0, 10) {
      if (R > N || R > M) continue;
      vvc<mint> A = random_matrix<mint>(N, M, R);
      vc<tuple<int, int, mint>> mat;
      FOR(i, N) FOR(j, M) mat.eb(i, j, A[i][j]);
      vc<mint> x(N), y(M);
      FOR(i, M) y[i] = RNG(0, mint::get_mod());
      FOR(i, N) FOR(j, M) x[i] += A[i][j] * y[j];
      if (RNG(0, 2) == 0) { FOR(i, M) y[i] = RNG(0, 2); }
      int fail = 0;
      FOR(5) {
        vc<mint> ans = sparse_solve_linear<mint>(N, M, mat, x);
        if (ans.empty()) ++fail;
      }
      assert(fail <= 1);
    }
  }
}

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

signed main() {
  test();
  solve();
  return 0;
}

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