Problem p02563 (C++) — buggy submission, verdict: Runtime Error

#include <bits/stdc++.h>
#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
  int x = 0;
  while ((1U << x) < (unsigned int)(n))
    x++;
  return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
  unsigned long index;
  _BitScanForward(&index, n);
  return index;
#else
  return __builtin_ctz(n);
#endif
}

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_BITOP_HPP

#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1

#include <utility>

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
  x %= m;
  if (x < 0)
    x += m;
  return x;
}

// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
  unsigned int _m;
  unsigned long long im;

  // @param m `1 <= m`
  barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

  // @return m
  unsigned int umod() const { return _m; }

  // @param a `0 <= a < m`
  // @param b `0 <= b < m`
  // @return `a * b % m`
  unsigned int mul(unsigned int a, unsigned int b) const {
    // [1] m = 1
    // a = b = im = 0, so okay

    // [2] m >= 2
    // im = ceil(2^64 / m)
    // -> im * m = 2^64 + r (0 <= r < m)
    // let z = a*b = c*m + d (0 <= c, d < m)
    // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
    // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) <
    // 2^64 * 2
    // ((ab * im) >> 64) == c or c + 1
    unsigned long long z = a;
    z *= b;
#ifdef _MSC_VER
    unsigned long long x;
    _umul128(z, im, &x);
#else
    unsigned long long x =
        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
    unsigned int v = (unsigned int)(z - x * _m);
    if (_m <= v)
      v += _m;
    return v;
  }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
  if (m == 1)
    return 0;
  unsigned int _m = (unsigned int)(m);
  unsigned long long r = 1;
  unsigned long long y = safe_mod(x, m);
  while (n) {
    if (n & 1)
      r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
  if (n <= 1)
    return false;
  if (n == 2 || n == 7 || n == 61)
    return true;
  if (n % 2 == 0)
    return false;
  long long d = n - 1;
  while (d % 2 == 0)
    d /= 2;
  for (long long a : {2, 7, 61}) {
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
  a = safe_mod(a, b);
  if (a == 0)
    return {b, 0};

  // Contracts:
  // [1] s - m0 * a = 0 (mod b)
  // [2] t - m1 * a = 0 (mod b)
  // [3] s * |m1| + t * |m0| <= b
  long long s = b, t = a;
  long long m0 = 0, m1 = 1;

  while (t) {
    long long u = s / t;
    s -= t * u;
    m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b

    // [3]:
    // (s - t * u) * |m1| + t * |m0 - m1 * u|
    // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
    // = s * |m1| + t * |m0| <= b

    auto tmp = s;
    s = t;
    t = tmp;
    tmp = m0;
    m0 = m1;
    m1 = tmp;
  }
  // by [3]: |m0| <= b/g
  // by g != b: |m0| < b/g
  if (m0 < 0)
    m0 += b / s;
  return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
  if (m == 2)
    return 1;
  if (m == 167772161)
    return 3;
  if (m == 469762049)
    return 3;
  if (m == 754974721)
    return 11;
  if (m == 998244353)
    return 3;
  int divs[20] = {};
  divs[0] = 2;
  int cnt = 1;
  int x = (m - 1) / 2;
  while (x % 2 == 0)
    x /= 2;
  for (int i = 3; (long long)(i)*i <= x; i += 2) {
    if (x % i == 0) {
      divs[cnt++] = i;
      while (x % i == 0) {
        x /= i;
      }
    }
  }
  if (x > 1) {
    divs[cnt++] = x;
  }
  for (int g = 2;; g++) {
    bool ok = true;
    for (int i = 0; i < cnt; i++) {
      if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
        ok = false;
        break;
      }
    }
    if (ok)
      return g;
  }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_MATH_HPP

#ifndef ATCODER_INTERNAL_SCC_HPP
#define ATCODER_INTERNAL_SCC_HPP 1

#include <algorithm>
#include <utility>
#include <vector>

namespace atcoder {
namespace internal {

template <class E> struct csr {
  std::vector<int> start;
  std::vector<E> elist;
  csr(int n, const std::vector<std::pair<int, E>> &edges)
      : start(n + 1), elist(edges.size()) {
    for (auto e : edges) {
      start[e.first + 1]++;
    }
    for (int i = 1; i <= n; i++) {
      start[i] += start[i - 1];
    }
    auto counter = start;
    for (auto e : edges) {
      elist[counter[e.first]++] = e.second;
    }
  }
};

// Reference:
// R. Tarjan,
// Depth-First Search and Linear Graph Algorithms
struct scc_graph {
public:
  scc_graph(int n) : _n(n) {}

  int num_vertices() { return _n; }

  void add_edge(int from, int to) { edges.push_back({from, {to}}); }

  // @return pair of (# of scc, scc id)
  std::pair<int, std::vector<int>> scc_ids() {
    auto g = csr<edge>(_n, edges);
    int now_ord = 0, group_num = 0;
    std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
    visited.reserve(_n);
    auto dfs = [&](auto self, int v) -> void {
      low[v] = ord[v] = now_ord++;
      visited.push_back(v);
      for (int i = g.start[v]; i < g.start[v + 1]; i++) {
        auto to = g.elist[i].to;
        if (ord[to] == -1) {
          self(self, to);
          low[v] = std::min(low[v], low[to]);
        } else {
          low[v] = std::min(low[v], ord[to]);
        }
      }
      if (low[v] == ord[v]) {
        while (true) {
          int u = visited.back();
          visited.pop_back();
          ord[u] = _n;
          ids[u] = group_num;
          if (u == v)
            break;
        }
        group_num++;
      }
    };
    for (int i = 0; i < _n; i++) {
      if (ord[i] == -1)
        dfs(dfs, i);
    }
    for (auto &x : ids) {
      x = group_num - 1 - x;
    }
    return {group_num, ids};
  }

  std::vector<std::vector<int>> scc() {
    auto ids = scc_ids();
    int group_num = ids.first;
    std::vector<int> counts(group_num);
    for (auto x : ids.second)
      counts[x]++;
    std::vector<std::vector<int>> groups(ids.first);
    for (int i = 0; i < group_num; i++) {
      groups[i].reserve(counts[i]);
    }
    for (int i = 0; i < _n; i++) {
      groups[ids.second[i]].push_back(i);
    }
    return groups;
  }

private:
  int _n;
  struct edge {
    int to;
  };
  std::vector<std::pair<int, edge>> edges;
};

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_SCC_HPP

#ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP
#define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1

#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  is_signed_int128<T>::value ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_signed_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_signed<T>::value) ||
                                  is_signed_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value, make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using to_unsigned =
    typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_TYPE_TRAITS_HPP

#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1

// #include <atcoder/internal_math>
// #include <atcoder/internal_type_traits>
#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

} // namespace internal

template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
  using mint = static_modint;

public:
  static constexpr int mod() { return m; }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }

  static_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T> * = nullptr>
  static_modint(T v) {
    long long x = (long long)(v % (long long)(umod()));
    if (x < 0)
      x += umod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T> * = nullptr>
  static_modint(T v) {
    _v = (unsigned int)(v % umod());
  }
  static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }

  unsigned int val() const { return _v; }

  mint &operator++() {
    _v++;
    if (_v == umod())
      _v = 0;
    return *this;
  }
  mint &operator--() {
    if (_v == 0)
      _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }

  mint &operator+=(const mint &rhs) {
    _v += rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint &operator-=(const mint &rhs) {
    _v -= rhs._v;
    if (_v >= umod())
      _v += umod();
    return *this;
  }
  mint &operator*=(const mint &rhs) {
    unsigned long long z = _v;
    z *= rhs._v;
    _v = (unsigned int)(z % umod());
    return *this;
  }
  mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }

  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    if (prime) {
      assert(_v);
      return pow(umod() - 2);
    } else {
      auto eg = internal::inv_gcd(_v, m);
      assert(eg.first == 1);
      return eg.second;
    }
  }

  friend mint operator+(const mint &lhs, const mint &rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint &lhs, const mint &rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint &lhs, const mint &rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint &lhs, const mint &rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint &lhs, const mint &rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint &lhs, const mint &rhs) {
    return lhs._v != rhs._v;
  }

private:
  unsigned int _v;
  static constexpr unsigned int umod() { return m; }
  static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
  using mint = dynamic_modint;

public:
  static int mod() { return (int)(bt.umod()); }
  static void set_mod(int m) {
    assert(1 <= m);
    bt = internal::barrett(m);
  }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }

  dynamic_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T> * = nullptr>
  dynamic_modint(T v) {
    long long x = (long long)(v % (long long)(mod()));
    if (x < 0)
      x += mod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T> * = nullptr>
  dynamic_modint(T v) {
    _v = (unsigned int)(v % mod());
  }
  dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }

  unsigned int val() const { return _v; }

  mint &operator++() {
    _v++;
    if (_v == umod())
      _v = 0;
    return *this;
  }
  mint &operator--() {
    if (_v == 0)
      _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }

  mint &operator+=(const mint &rhs) {
    _v += rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint &operator-=(const mint &rhs) {
    _v += mod() - rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint &operator*=(const mint &rhs) {
    _v = bt.mul(_v, rhs._v);
    return *this;
  }
  mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }

  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    auto eg = internal::inv_gcd(_v, mod());
    assert(eg.first == 1);
    return eg.second;
  }

  friend mint operator+(const mint &lhs, const mint &rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint &lhs, const mint &rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint &lhs, const mint &rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint &lhs, const mint &rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint &lhs, const mint &rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint &lhs, const mint &rhs) {
    return lhs._v != rhs._v;
  }

private:
  unsigned int _v;
  static internal::barrett bt;
  static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

} // namespace internal

} // namespace atcoder

#endif // ATCODER_MODINT_HPP

#ifndef ATCODER_MATH_HPP
#define ATCODER_MATH_HPP 1

#include <algorithm>
#include <cassert>
#include <tuple>
#include <vector>
// #include <atcoder/internal_math>

namespace atcoder {

long long pow_mod(long long x, long long n, int m) {
  assert(0 <= n && 1 <= m);
  if (m == 1)
    return 0;
  internal::barrett bt((unsigned int)(m));
  unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
  while (n) {
    if (n & 1)
      r = bt.mul(r, y);
    y = bt.mul(y, y);
    n >>= 1;
  }
  return r;
}

long long inv_mod(long long x, long long m) {
  assert(1 <= m);
  auto z = internal::inv_gcd(x, m);
  assert(z.first == 1);
  return z.second;
}

// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long> &r,
                                    const std::vector<long long> &m) {
  assert(r.size() == m.size());
  int n = int(r.size());
  // Contracts: 0 <= r0 < m0
  long long r0 = 0, m0 = 1;
  for (int i = 0; i < n; i++) {
    assert(1 <= m[i]);
    long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
    if (m0 < m1) {
      std::swap(r0, r1);
      std::swap(m0, m1);
    }
    if (m0 % m1 == 0) {
      if (r0 % m1 != r1)
        return {0, 0};
      continue;
    }
    // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)

    // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
    // r2 % m0 = r0
    // r2 % m1 = r1
    // -> (r0 + x*m0) % m1 = r1
    // -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1)
    // -> x = (r1 - r0) / g * inv(u0) (mod u1)

    // im = inv(u0) (mod u1) (0 <= im < u1)
    long long g, im;
    std::tie(g, im) = internal::inv_gcd(m0, m1);

    long long u1 = (m1 / g);
    // |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
    if ((r1 - r0) % g)
      return {0, 0};

    // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
    long long x = (r1 - r0) / g % u1 * im % u1;

    // |r0| + |m0 * x|
    // < m0 + m0 * (u1 - 1)
    // = m0 + m0 * m1 / g - m0
    // = lcm(m0, m1)
    r0 += x * m0;
    m0 *= u1; // -> lcm(m0, m1)
    if (r0 < 0)
      r0 += m0;
  }
  return {r0, m0};
}

long long floor_sum(long long n, long long m, long long a, long long b) {
  long long ans = 0;
  if (a >= m) {
    ans += (n - 1) * n * (a / m) / 2;
    a %= m;
  }
  if (b >= m) {
    ans += n * (b / m);
    b %= m;
  }

  long long y_max = (a * n + b) / m, x_max = (y_max * m - b);
  if (y_max == 0)
    return ans;
  ans += (n - (x_max + a - 1) / a) * y_max;
  ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
  return ans;
}

} // namespace atcoder

#endif // ATCODER_MATH_HPP

#ifndef ATCODER_CONVOLUTION_HPP
#define ATCODER_CONVOLUTION_HPP 1

#include <algorithm>
#include <array>
// #include <atcoder/internal_bit>
// #include <atcoder/modint>
#include <cassert>
#include <type_traits>
#include <vector>

namespace atcoder {

namespace internal {

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly(std::vector<mint> &a) {
  static constexpr int g = internal::primitive_root<mint::mod()>;
  int n = int(a.size());
  int h = internal::ceil_pow2(n);

  static bool first = true;
  static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
  if (first) {
    first = false;
    mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
    int cnt2 = bsf(mint::mod() - 1);
    mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
    for (int i = cnt2; i >= 2; i--) {
      // e^(2^i) == 1
      es[i - 2] = e;
      ies[i - 2] = ie;
      e *= e;
      ie *= ie;
    }
    mint now = 1;
    for (int i = 0; i < cnt2 - 2; i++) {
      sum_e[i] = es[i] * now;
      now *= ies[i];
    }
  }
  for (int ph = 1; ph <= h; ph++) {
    int w = 1 << (ph - 1), p = 1 << (h - ph);
    mint now = 1;
    for (int s = 0; s < w; s++) {
      int offset = s << (h - ph + 1);
      for (int i = 0; i < p; i++) {
        auto l = a[i + offset];
        auto r = a[i + offset + p] * now;
        a[i + offset] = l + r;
        a[i + offset + p] = l - r;
      }
      now *= sum_e[bsf(~(unsigned int)(s))];
    }
  }
}

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly_inv(std::vector<mint> &a) {
  static constexpr int g = internal::primitive_root<mint::mod()>;
  int n = int(a.size());
  int h = internal::ceil_pow2(n);

  static bool first = true;
  static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
  if (first) {
    first = false;
    mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
    int cnt2 = bsf(mint::mod() - 1);
    mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
    for (int i = cnt2; i >= 2; i--) {
      // e^(2^i) == 1
      es[i - 2] = e;
      ies[i - 2] = ie;
      e *= e;
      ie *= ie;
    }
    mint now = 1;
    for (int i = 0; i < cnt2 - 2; i++) {
      sum_ie[i] = ies[i] * now;
      now *= es[i];
    }
  }

  for (int ph = h; ph >= 1; ph--) {
    int w = 1 << (ph - 1), p = 1 << (h - ph);
    mint inow = 1;
    for (int s = 0; s < w; s++) {
      int offset = s << (h - ph + 1);
      for (int i = 0; i < p; i++) {
        auto l = a[i + offset];
        auto r = a[i + offset + p];
        a[i + offset] = l + r;
        a[i + offset + p] =
            (unsigned long long)(mint::mod() + l.val() - r.val()) * inow.val();
      }
      inow *= sum_ie[bsf(~(unsigned int)(s))];
    }
  }
}

} // namespace internal

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m)
    return {};
  if (std::min(n, m) <= 60) {
    if (n < m) {
      std::swap(n, m);
      std::swap(a, b);
    }
    std::vector<mint> ans(n + m - 1);
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ans[i + j] += a[i] * b[j];
      }
    }
    return ans;
  }
  int z = 1 << internal::ceil_pow2(n + m - 1);
  a.resize(z);
  internal::butterfly(a);
  b.resize(z);
  internal::butterfly(b);
  for (int i = 0; i < z; i++) {
    a[i] *= b[i];
  }
  internal::butterfly_inv(a);
  a.resize(n + m - 1);
  mint iz = mint(z).inv();
  for (int i = 0; i < n + m - 1; i++)
    a[i] *= iz;
  return a;
}

template <unsigned int mod = 998244353, class T,
          std::enable_if_t<internal::is_integral<T>::value> * = nullptr>
std::vector<T> convolution(const std::vector<T> &a, const std::vector<T> &b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m)
    return {};

  using mint = static_modint<mod>;
  std::vector<mint> a2(n), b2(m);
  for (int i = 0; i < n; i++) {
    a2[i] = mint(a[i]);
  }
  for (int i = 0; i < m; i++) {
    b2[i] = mint(b[i]);
  }
  auto c2 = convolution(move(a2), move(b2));
  std::vector<T> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    c[i] = c2[i].val();
  }
  return c;
}

std::vector<long long> convolution_ll(const std::vector<long long> &a,
                                      const std::vector<long long> &b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m)
    return {};

  static constexpr unsigned long long MOD1 = 754974721; // 2^24
  static constexpr unsigned long long MOD2 = 167772161; // 2^25
  static constexpr unsigned long long MOD3 = 469762049; // 2^26
  static constexpr unsigned long long M2M3 = MOD2 * MOD3;
  static constexpr unsigned long long M1M3 = MOD1 * MOD3;
  static constexpr unsigned long long M1M2 = MOD1 * MOD2;
  static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

  static constexpr unsigned long long i1 =
      internal::inv_gcd(MOD2 * MOD3, MOD1).second;
  static constexpr unsigned long long i2 =
      internal::inv_gcd(MOD1 * MOD3, MOD2).second;
  static constexpr unsigned long long i3 =
      internal::inv_gcd(MOD1 * MOD2, MOD3).second;

  auto c1 = convolution<MOD1>(a, b);
  auto c2 = convolution<MOD2>(a, b);
  auto c3 = convolution<MOD3>(a, b);

  std::vector<long long> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    unsigned long long x = 0;
    x += (c1[i] * i1) % MOD1 * M2M3;
    x += (c2[i] * i2) % MOD2 * M1M3;
    x += (c3[i] * i3) % MOD3 * M1M2;
    // B = 2^63, -B <= x, r(real value) < B
    // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
    // r = c1[i] (mod MOD1)
    // focus on MOD1
    // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
    // r = x,
    //     x - M' + (0 or 2B),
    //     x - 2M' + (0, 2B or 4B),
    //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
    // (r - x) = 0, (0)
    //           - M' + (0 or 2B), (1)
    //           -2M' + (0 or 2B or 4B), (2)
    //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
    // we checked that
    //   ((1) mod MOD1) mod 5 = 2
    //   ((2) mod MOD1) mod 5 = 3
    //   ((3) mod MOD1) mod 5 = 4
    long long diff =
        c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
    if (diff < 0)
      diff += MOD1;
    static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3,
                                                     3 * M1M2M3};
    x -= offset[diff % 5];
    c[i] = x;
  }

  return c;
}

} // namespace atcoder

#endif // ATCODER_CONVOLUTION_HPP

using namespace std;
using namespace atcoder;

int main() {
  int N, M;
  cin >> N >> M;
  vector<int> a(N), b(M);
  for (int i = 0; i < N; i++)
    cin >> a[i];
  for (int i = 0; i < M; i++)
    cin >> b[i];
  vector<int> c = convolution<998244353>(a, b);
  for (int i; i < c.size(); i++) {
    if (i)
      cout << " ";
    cout << c[i];
  }
  cout << endl;
}

Error: -6
c282713f-861e-43f8-9afb-3d3e46c0d6e8.out: /home/alex/Documents/bug-detection/input/Project_CodeNet/data/p02563/C++/s857793398.cpp:25: bool atcoder::dsu::same(int, int): Assertion `0 <= a && a < _n' failed.


Fixed submission:

#include <bits/stdc++.h>
namespace atcoder {

// Implement (union by size) + (path compression)
// Reference:
// Zvi Galil and Giuseppe F. Italiano,
// Data structures and algorithms for disjoint set union problems
struct dsu {
public:
  dsu() : _n(0) {}
  dsu(int n) : _n(n), parent_or_size(n, -1) {}

  int merge(int a, int b) {
    assert(0 <= a && a < _n);
    assert(0 <= b && b < _n);
    int x = leader(a), y = leader(b);
    if (x == y)
      return x;
    if (-parent_or_size[x] < -parent_or_size[y])
      std::swap(x, y);
    parent_or_size[x] += parent_or_size[y];
    parent_or_size[y] = x;
    return x;
  }

  bool same(int a, int b) {
    assert(0 <= a && a < _n);
    assert(0 <= b && b < _n);
    return leader(a) == leader(b);
  }

  int leader(int a) {
    assert(0 <= a && a < _n);
    if (parent_or_size[a] < 0)
      return a;
    return parent_or_size[a] = leader(parent_or_size[a]);
  }

  int size(int a) {
    assert(0 <= a && a < _n);
    return -parent_or_size[leader(a)];
  }

  std::vector<std::vector<int>> groups() {
    std::vector<int> leader_buf(_n), group_size(_n);
    for (int i = 0; i < _n; i++) {
      leader_buf[i] = leader(i);
      group_size[leader_buf[i]]++;
    }
    std::vector<std::vector<int>> result(_n);
    for (int i = 0; i < _n; i++) {
      result[i].reserve(group_size[i]);
    }
    for (int i = 0; i < _n; i++) {
      result[leader_buf[i]].push_back(i);
    }
    result.erase(
        std::remove_if(result.begin(), result.end(),
                       [&](const std::vector<int> &v) { return v.empty(); }),
        result.end());
    return result;
  }

private:
  int _n;
  // root node: -1 * component size
  // otherwise: parent
  std::vector<int> parent_or_size;
};

} // namespace atcoder
using namespace std;
using namespace atcoder;

int main() {
  // 0-ind
  int N, Q;
  cin >> N >> Q;
  dsu d(N);
  while (Q--) {
    int t, u, v;
    cin >> t >> u >> v;
    if (t == 0) {
      d.merge(u, v);
    } else {
      cout << d.same(u, v) << endl;
    }
  }
}