Language: C++

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author zjsdut
 */

#if not defined LOCAL and not defined NDEBUG
#define NDEBUG
#endif
extern const bool show_all_failed_tests = false;
extern const bool compare_real_numbers = false;
#ifndef CP_UTILS
#define CP_UTILS
#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstring>
#include <map>
#include <numeric>
#include <set>
//
// Created by zjsdu on 5/28/2020.
//

#ifndef JHELPER_EXAMPLE_PROJECT_LIBRARY_ALIAS_HPP_
#define JHELPER_EXAMPLE_PROJECT_LIBRARY_ALIAS_HPP_
#include <string>
#include <cassert>
#include <queue>
#ifndef JHELPER_EXAMPLE_PROJECT_LIBRARY_IO_HPP_
#define JHELPER_EXAMPLE_PROJECT_LIBRARY_IO_HPP_
#include <iostream>
#include <vector>
#include <tuple>
struct fast_ios {
  fast_ios() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
    std::cout.precision(10);
    std::cout << std::fixed;
  };
} fast_ios_;
namespace io {
template<typename... Ts>
std::istream &operator>>(std::istream &in, std::tuple<Ts...> &t);
template<typename T, typename U>
std::istream &operator>>(std::istream &in, std::pair<T, U> &p) {
  in >> p.first >> p.second;
  return in;
}

template<typename T>
std::istream &operator>>(std::istream &stream, std::vector<T> &vec) {
  for (auto &x : vec)
    stream >> x;
  return stream;
}

template<typename... Ts>
std::istream &operator>>(std::istream &in, const std::tuple<Ts...> &t) {
  std::apply([&in](auto &... args) { ((in >> args), ...); }, t);
  return in;
}

template<class... Args> void scan(Args &... args) {
  ((std::cin >> args), ...);
}

template<typename T>
std::ostream &operator<<(std::ostream &out, const std::vector<T> &vec) {
  bool first = true;
  for (const T &t : vec) {
    if (first)
      first = false;
    else
      out << ' ';
    out << t;
  }
  return out;
}

template<typename T, typename U>
std::ostream &operator<<(std::ostream &out, const std::pair<T, U> &p) {
  out << p.first << ' ' << p.second;
  return out;
}

template<typename T>
std::ostream &operator<<(std::ostream &out,
                         const std::vector<std::vector<T>> &t) {
  bool is_first = true;
  for (const auto &row : t) {
    if (is_first)
      is_first = false;
    else
      out << '\n';
    out << row;
  }
  return out;
}

template<typename... Args> void pt(Args &&... args) {
  ((std::cout << args << ' '), ...);
}

template<typename First, typename... Args>
void pl(const First &first, const Args &... args) {
  std::cout << first;
  ((std::cout << ' ' << args), ...);
  std::cout << '\n';
}

template<typename... Args> void pn(const Args &... args) {
  ((std::cout << args << '\n'), ...);
}
}// namespace io
inline int ri() {
  int x;
  std::cin >> x;
  return x;
}
#endif// JHELPER_EXAMPLE_PROJECT_LIBRARY_IO_HPP_

using ll = long long;
using ull = unsigned long long;
using vl = std::vector<ll>;
using vb = std::vector<bool>;
using vi = std::vector<int>;
using vs = std::vector<std::string>;
using pii = std::pair<int, int>;
using pli = std::pair<ll, int>;
using pil = std::pair<int, ll>;
using pll = std::pair<ll, ll>;
using vii = std::vector<pii>;
template<typename T, typename U = std::less<T>>
using pq = std::priority_queue<T, std::vector<T>, U>;
template<typename... Ts> using vt = std::vector<std::tuple<Ts...>>;
template<typename T> class vv {
  std::vector<std::vector<T>> data;
  int n, m;

 public:
  explicit vv(int n) : n(n), m(0) {
    assert(n > 0);
    data.assign(n, std::vector<T>{});
  }
  vv(int n, int m, T init = T{}) : n(n), m(m) {
    assert(n > 0 && m > 0);
    data.assign(n, std::vector<T>(m, init));
  }
  std::vector<T> &operator[](size_t i) {
    assert(i < n);
    return data[i];
  }
  const std::vector<T> &operator[](size_t i) const {
    assert(i < n);
    return data[i];
  }
  void fill(T val) {
    for (auto &row : data)
      std::fill(row.begin(), row.end(), val);
  }
  vv<T> transpose() const {
    assert(m > 0);
    vv<T> ret(m, n);
    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        ret.data[i][j] = data[j][i];
    return ret;
  }
  friend std::istream &operator>>(std::istream &in, vv<T> &val) {
    return io::operator>>(in, val.data);
  }
  friend std::ostream &operator<<(std::ostream &out, const vv<T> &val) {
    return io::operator<<(out, val.data);
  }
  friend auto begin(vv<T> &val) { return val.data.begin(); }
  friend auto end(vv<T> &val) { return val.data.end(); }
  friend auto rbegin(vv<T> &val) { return val.data.rbegin(); }
  friend auto rend(vv<T> &val) { return val.data.rend(); }
};
#define TOKENPASTE(x, y) x##y
#define TOKENPASTE2(x, y) TOKENPASTE(x, y)
#define rng3(i, a, b)                                                          \
  for (std::common_type<decltype(a), decltype(b)>::type                        \
           i = a,                                                              \
           TOKENPASTE2(r_end_, __LINE__) = b;                                  \
       i < TOKENPASTE2(r_end_, __LINE__); ++i)
#define rng2(i, n) rng3(i, 0, n)
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define rng(...) GET_MACRO(__VA_ARGS__, rng3, rng2)(__VA_ARGS__)
#define up(i, a, b)                                                            \
  for (std::common_type<decltype(a), decltype(b)>::type                        \
           i = a,                                                              \
           TOKENPASTE2(r_end_, __LINE__) = b;                                  \
       i <= TOKENPASTE2(r_end_, __LINE__); ++i)
#define down(i, b, a)                                                          \
  for (std::common_type<decltype(a), decltype(b)>::type                        \
           i = b,                                                              \
           TOKENPASTE2(r_end_, __LINE__) = a;                                  \
       i >= TOKENPASTE2(r_end_, __LINE__); --i)
#define rep(n)                                                                 \
  for (auto TOKENPASTE2(_iter_, __LINE__) = n;                                 \
       TOKENPASTE2(_iter_, __LINE__) > 0; --TOKENPASTE2(_iter_, __LINE__))
#define FOR(x, cont) for (const auto &x : cont)
#define For(x, cont) for (auto &x : cont)
#define ALL(x) begin(x), end(x)
// hat off to 300iq
#define RALL(x) rbegin(x), rend(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ep emplace
#define SZ(x) (int) (x).size()
#define rp(...) return pl(__VA_ARGS__)
#define rpn(...) return pn(__VA_ARGS__)
#define adv(i, n)                                                              \
  for (auto TOKENPASTE2(_n_, __LINE__) = n; i < TOKENPASTE2(_n_, __LINE__); ++i)
#define INT(...)                                                               \
  int __VA_ARGS__;                                                             \
  scan(__VA_ARGS__)
#define LL(...)                                                                \
  long long __VA_ARGS__;                                                       \
  scan(__VA_ARGS__)
#define STR(...)                                                               \
  std::string __VA_ARGS__;                                                     \
  scan(__VA_ARGS__)
#endif// JHELPER_EXAMPLE_PROJECT_LIBRARY_ALIAS_HPP_

inline void Yn(bool p) {
  std::cout << (p ? "Yes\n" : "No\n");
}
inline void YN(bool p) {
  std::cout << (p ? "YES\n" : "NO\n");
}
inline void yn(bool p) {
  std::cout << (p ? "yes\n" : "no\n");
}
template<typename T> T &inc(T &cont) {
  for (auto &e : cont)
    ++e;
  return cont;
}
template<typename T> T &dec(T &cont) {
  for (auto &e : cont)
    --e;
  return cont;
}
template<typename A, typename B> inline bool chkmin(A &a, const B &b) {
  return b < a ? a = b, true : false;
}

template<typename A, typename B> inline bool chkmax(A &a, const B &b) {
  return a < b ? a = b, true : false;
}

template <typename Container> Container& rev(Container& c) {
  std::reverse(std::begin(c), std::end(c));
  return c;
}

template <typename Container> auto max(const Container&  c) {
  return *std::max_element(std::begin(c), std::end(c));
}

template <typename Container> auto min(const Container& c) {
  return *std::min_element(std::begin(c), std::end(c));
}

template<typename T> struct reversion_wrapper { T &iterable; };
template<typename T> auto begin(reversion_wrapper<T> w) {
  using std::rbegin;
  return rbegin(w.iterable);
}
template<typename T> auto end(reversion_wrapper<T> w) {
  using std::rend;
  return rend(w.iterable);
}
template<typename T> reversion_wrapper<T> reverse(T &&iterable) {
  return {iterable};
}
template<typename T, typename U> T ceil(T x, U y) {
  assert(y > 0);
  if (x > 0)
    x += y - 1;
  return x / y;
}

template<typename T, typename U> T floor(T x, U y) {
  assert(y > 0);
  if (x < 0)
    x -= y - 1;
  return x / y;
}

template<class...> struct typelist {};

template<class T, class... Ts>
constexpr bool any_same = (std::is_same_v<T, Ts> || ...);

template<class F> struct y_combinator {
  template<class... TLs> struct ref {
    y_combinator &self;
    template<class... Args> decltype(auto) operator()(Args &&... args) const {
      using G = std::conditional_t<any_same<typelist<Args...>, TLs...>,
                                   ref<TLs...>, ref<TLs..., typelist<Args...>>>;
      return self.f(G{self}, std::forward<Args>(args)...);
    }
  };
  F f;
  template<class... Args> decltype(auto) operator()(Args &&... args) {
    return ref<>{*this}(std::forward<Args>(args)...);
  }
};
template<class F> y_combinator(F) -> y_combinator<F>;
#ifndef debug
#define debug(...) 42
#endif
#ifndef show
#define show(...) 42
#endif
using namespace io;
using namespace std;
#endif// CP_UTILS

//
// Created by zjsdu on 7/1/2020.
//

#ifndef JHELPER_EXAMPLE_PROJECT_LIBRARY_NTT_HPP_
#define JHELPER_EXAMPLE_PROJECT_LIBRARY_NTT_HPP_
#ifndef ALGO_MODULAR
#define ALGO_MODULAR


// tourist's modular-arithmetic class
template<typename T> T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    std::swap(a, m);
    u -= t * v;
    std::swap(u, v);
  }
  assert(m == 1);
  return u;
}

template<typename T> class Modular {
 public:
  using Type = typename std::decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}

  template<typename U> Modular(const U &x) { value = normalize(x); }

  template<typename U> static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0)
      v += mod();
    return v;
  }

  const Type &operator()() const { return value; }

  template<typename U> explicit operator U() const {
    return static_cast<U>(value);
  }

  constexpr static Type mod() { return T::value; }

  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod())
      value -= mod();
    return *this;
  }

  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0)
      value += mod();
    return *this;
  }

  template<typename U> Modular &operator+=(const U &other) {
    return *this += Modular(other);
  }

  template<typename U> Modular &operator-=(const U &other) {
    return *this -= Modular(other);
  }

  Modular &operator++() { return *this += 1; }

  Modular &operator--() { return *this -= 1; }

  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }

  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }

  Modular operator-() const { return Modular(-value); }

  template<typename U = T>
  typename std::enable_if<std::is_same<typename Modular<U>::Type, int>::value,
                          Modular>::type &
  operator*=(const Modular &rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x),
             d, m;
    asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod()));
    value = m;
#else
    value = normalize(static_cast<int64_t>(value)
                      * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }

  template<typename U = T>
  typename std::enable_if<
      std::is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type &
  operator*=(const Modular &rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value
                                     / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }

  template<typename U = T>
  typename std::enable_if<!std::is_integral<typename Modular<U>::Type>::value,
                          Modular>::type &
  operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular &operator/=(const Modular &other) {
    return *this *= Modular(inverse(other.value, mod()));
  }

  template<typename U> friend const Modular<U> &abs(const Modular<U> &v) {
    return v;
  }

  template<typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

  template<typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

  template<typename U>
  friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

 private:
  Type value;
};

template<typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value == rhs.value;
}

template<typename T, typename U> bool operator==(const Modular<T> &lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}

template<typename T, typename U> bool operator==(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) == rhs;
}

template<typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template<typename T, typename U> bool operator!=(const Modular<T> &lhs, U rhs) {
  return !(lhs == rhs);
}

template<typename T, typename U> bool operator!=(U lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template<typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value < rhs.value;
}

template<typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template<typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}

template<typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template<typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template<typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}

template<typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template<typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template<typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}

template<typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template<typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template<typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}

template<typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template<typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1)
      res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template<typename T> bool IsZero(const Modular<T> &number) {
  return number() == 0;
}

template<typename T> std::string to_string(const Modular<T> &number) {
  return std::to_string(number());
}

template<typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
  return stream << number();
}

template<typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
  typename std::common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

template<int md>
using Mint = Modular<
    std::integral_constant<typename std::decay<decltype(md)>::type, md>>;
using ModType = int;
struct VarMod {
  static ModType value;
};
ModType VarMod::value;
ModType &md = VarMod::value;
#endif

template<typename T> class NTT {
 public:
  using Type = typename std::decay<decltype(T::value)>::type;
  // md must be a prime.
  static Type md;
  static Modular<T> root;
  static int base;
  static int max_base;
  static std::vector<Modular<T>> roots;
  static std::vector<int> rev;
  static void clear() {
    root = 0;
    base = 0;
    max_base = 0;
    roots.clear();
    rev.clear();
  }
  static void init() {
    md = T::value;
    assert(md >= 3 && md % 2 == 1);
    auto tmp = md - 1;
    max_base = 0;
    // md - 1 == c * 2 ^ max_base
    while (tmp % 2 == 0) {
      tmp /= 2;
      max_base++;
    }
    root = 2;
    //　root: an element of order 2 ^ max_base
    while (power(root, (md - 1) >> 1) == 1) {
      root++;
    }
    assert(power(root, md - 1) == 1);
    root = power(root, (md - 1) >> max_base);
    base = 1;
    rev = {0, 1};
    roots = {0, 1};
  }
  static void ensure_base(int nbase) {
    if (md != T::value) {
      clear();
    }
    if (roots.empty()) {
      init();
    }
    if (nbase <= base) {
      return;
    }
    assert(nbase <= max_base);
    // rev[i] := bit_reverse(i)
    rev.resize(1 << nbase);
    for (int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    roots.resize(1 << nbase);
    // 计算长度为2k的变换，需要用到一个2k阶元的0到k-1次方
    // roots[k+i] := 2k阶元的i次方
    while (base < nbase) {
      Modular<T> z = power(root, 1 << (max_base - 1 - base));
      for (int i = 1 << (base - 1); i < (1 << base); i++) {
        roots[i << 1] = roots[i];
        roots[(i << 1) + 1] = roots[i] * z;
      }
      base++;
    }
  }
  static void fft(std::vector<Modular<T>> &a) {
    int n = (int) a.size();
    // n is an exact power of 2.
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for (int i = 0; i < n; i++) {
      if (i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for (int k = 1; k < n; k <<= 1) {
      for (int i = 0; i < n; i += 2 * k) {
        for (int j = 0; j < k; j++) {
          Modular<T> x = a[i + j];
          Modular<T> y = a[i + j + k] * roots[j + k];
          a[i + j] = x + y;
          a[i + j + k] = x - y;
        }
      }
    }
  }
  static std::vector<Modular<T>> multiply(std::vector<Modular<T>> a,
                                          std::vector<Modular<T>> b) {
    if (a.empty() || b.empty()) {
      return {};
    }
    int eq = (a == b);
    int need = (int) a.size() + (int) b.size() - 1;
    int nbase = 0;
    while ((1 << nbase) < need)
      nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    a.resize(sz);
    b.resize(sz);
    fft(a);
    if (eq)
      b = a;
    else
      fft(b);
    Modular<T> inv_sz = 1 / static_cast<Modular<T>>(sz);
    for (int i = 0; i < sz; i++) {
      a[i] *= b[i] * inv_sz;
    }
    reverse(a.begin() + 1, a.end());
    fft(a);
    a.resize(need);
    return a;
  }
};
template<typename T> typename NTT<T>::Type NTT<T>::md;
template<typename T> Modular<T> NTT<T>::root;
template<typename T> int NTT<T>::base;
template<typename T> int NTT<T>::max_base;
template<typename T> std::vector<Modular<T>> NTT<T>::roots;
template<typename T> std::vector<int> NTT<T>::rev;

template<typename T>
std::vector<Modular<T>> inverse(const std::vector<Modular<T>> &a) {
  assert(!a.empty());
  int n = (int) a.size();
  std::vector<Modular<T>> b = {1 / a[0]};
  while ((int) b.size() < n) {
    std::vector<Modular<T>> x(a.begin(),
                              a.begin() + min(a.size(), b.size() << 1));
    x.resize(b.size() << 1);
    b.resize(b.size() << 1);
    std::vector<Modular<T>> c = b;
    NTT<T>::fft(c);
    NTT<T>::fft(x);
    Modular<T> inv = 1 / static_cast<Modular<T>>((int) x.size());
    for (int i = 0; i < (int) x.size(); i++) {
      x[i] *= c[i] * inv;
    }
    reverse(x.begin() + 1, x.end());
    NTT<T>::fft(x);
    rotate(x.begin(), x.begin() + (x.size() >> 1), x.end());
    fill(x.begin() + (x.size() >> 1), x.end(), 0);
    NTT<T>::fft(x);
    for (int i = 0; i < (int) x.size(); i++) {
      x[i] *= c[i] * inv;
    }
    reverse(x.begin() + 1, x.end());
    NTT<T>::fft(x);
    for (int i = 0; i < ((int) x.size() >> 1); i++) {
      b[i + ((int) x.size() >> 1)] = -x[i];
    }
  }
  b.resize(n);
  return b;
}
template<typename T>
std::vector<Modular<T>> inverse_old(std::vector<Modular<T>> a) {
  assert(!a.empty());
  int n = (int) a.size();
  if (n == 1) {
    return {1 / a[0]};
  }
  int m = (n + 1) >> 1;
  std::vector<Modular<T>> b =
      inverse(std::vector<Modular<T>>(a.begin(), a.begin() + m));
  int need = n << 1;
  int nbase = 0;
  while ((1 << nbase) < need) {
    ++nbase;
  }
  NTT<T>::ensure_base(nbase);
  int size = 1 << nbase;
  a.resize(size);
  b.resize(size);
  NTT<T>::fft(a);
  NTT<T>::fft(b);
  Modular<T> inv = 1 / static_cast<Modular<T>>(size);
  for (int i = 0; i < size; ++i) {
    a[i] = (2 - a[i] * b[i]) * b[i] * inv;
  }
  reverse(a.begin() + 1, a.end());
  NTT<T>::fft(a);
  a.resize(n);
  return a;
}
template<typename T>
std::vector<Modular<T>> operator*(const std::vector<Modular<T>> &a,
                                  const std::vector<Modular<T>> &b) {
  if (a.empty() || b.empty()) {
    return {};
  }
  if (std::min(a.size(), b.size()) < 150) {
    std::vector<Modular<T>> c(a.size() + b.size() - 1, 0);
    for (int i = 0; i < (int) a.size(); i++) {
      for (int j = 0; j < (int) b.size(); j++) {
        c[i + j] += a[i] * b[j];
      }
    }
    return c;
  }
  return NTT<T>::multiply(a, b);
}
template<typename T>
std::vector<Modular<T>> &operator*=(std::vector<Modular<T>> &a,
                                    const std::vector<Modular<T>> &b) {
  return a = a * b;
}
#endif// JHELPER_EXAMPLE_PROJECT_LIBRARY_NTT_HPP_

using mint = Modular<integral_constant<ll, 75161927681>>;

void solve() {
  const int p = 200003, g = 2;
  vi index(p);
  for (int i = 0, x = 1; i < p - 1; ++i)
    index[x] = i, x = 1ll * g * x % p;
  vi cnt(p - 1);

  ll exclude = 0;
  INT (n);
  rep (n) {
    INT (x);
    if (x)
      cnt[index[x]]++, exclude += x * 1ll * x % p;
  }

  vector<mint> a(p - 1);
  rng (i, p - 1)
    a[i] = cnt[i];

  auto res = a * a;
  int t = 1;
  ll ans = 0;
  FOR (x, res) {
    ans += int(x) * t;
    t = t * 1ll * g % p;
  }
  pl((ans - exclude) / 2);

}
/*
 * Make sure that your laptop is plugged in or the build may be slow.
 *
 * Don't settle for a solution if it feels too clunky, take a moment and see if
 * you can make it simpler.
 */


int main() {
  solve();
  return 0;
}


Compiler output:
a.cc: In instantiation of 'Modular<T> operator*(const Modular<T>&, const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]':
a.cc:808:26:   required from 'std::vector<Modular<T> > operator*(const std::vector<Modular<T> >&, const std::vector<Modular<T> >&) [with T = std::integral_constant<long long int, 75161927681>]'
  808 |         c[i + j] += a[i] * b[j];
      |                     ~~~~~^~~~
a.cc:843:18:   required from here
  843 |   auto res = a * a;
      |                  ^
a.cc:535:26: error: no match for 'operator*=' (operand types are 'Modular<std::integral_constant<long long int, 75161927681> >' and 'const Modular<std::integral_constant<long long int, 75161927681> >')
  535 |   return Modular<T>(lhs) *= rhs;
      |          ~~~~~~~~~~~~~~~~^~~~~~
a.cc:419:3: note: candidate: 'template<class U> typename std::enable_if<std::is_same<typename Modular<U>::Type, int>::value, Modular<T> >::type& Modular<T>::operator*=(const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]'
  419 |   operator*=(const Modular &rhs) {
      |   ^~~~~~~~
a.cc:419:3: note:   template argument deduction/substitution failed:
a.cc: In substitution of 'template<class U> typename std::enable_if<std::is_same<typename Modular<T>::Type, int>::value, Modular<std::integral_constant<long long int, 75161927681> > >::type& Modular<std::integral_constant<long long int, 75161927681> >::operator*=(const Modular<std::integral_constant<long long int, 75161927681> >&) [with U = std::integral_constant<long long int, 75161927681>]':
a.cc:535:26:   required from 'Modular<T> operator*(const Modular<T>&, const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]'
  535 |   return Modular<T>(lhs) *= rhs;
      |          ~~~~~~~~~~~~~~~~^~~~~~
a.cc:808:26:   required from 'std::vector<Modular<T> > operator*(const std::vector<Modular<T> >&, const std::vector<Modular<T> >&) [with T = std::integral_constant<long long int, 75161927681>]'
  808 |         c[i + j] += a[i] * b[j];
      |                     ~~~~~^~~~
a.cc:843:18:   required from here
  843 |   auto res = a * a;
      |                  ^
a.cc:419:3: error: no type named 'type' in 'struct std::enable_if<false, Modular<std::integral_constant<long long int, 75161927681> > >'
  419 |   operator*=(const Modular &rhs) {
      |   ^~~~~~~~
a.cc: In instantiation of 'Modular<T> operator*(const Modular<T>&, const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]':
a.cc:808:26:   required from 'std::vector<Modular<T> > operator*(const std::vector<Modular<T> >&, const std::vector<Modular<T> >&) [with T = std::integral_constant<long long int, 75161927681>]'
  808 |         c[i + j] += a[i] * b[j];
      |                     ~~~~~^~~~
a.cc:843:18:   required from here
  843 |   auto res = a * a;
      |                  ^
a.cc:436:3: note: candidate: 'template<class U> typename std::enable_if<std::is_same<typename Modular<U>::Type, long int>::value, Modular<T> >::type& Modular<T>::operator*=(const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]'
  436 |   operator*=(const Modular &rhs) {
      |   ^~~~~~~~
a.cc:436:3: note:   template argument deduction/substitution failed:
a.cc: In substitution of 'template<class U> typename std::enable_if<std::is_same<typename Modular<T>::Type, long int>::value, Modular<std::integral_constant<long long int, 75161927681> > >::type& Modular<std::integral_constant<long long int, 75161927681> >::operator*=(const Modular<std::integral_constant<long long int, 75161927681> >&) [with U = std::integral_constant<long long int, 75161927681>]':
a.cc:535:26:   required from 'Modular<T> operator*(const Modular<T>&, const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]'
  535 |   return Modular<T>(lhs) *= rhs;
      |          ~~~~~~~~~~~~~~~~^~~~~~
a.cc:808:26:   required from 'std::vector<Modular<T> > operator*(const std::vector<Modular<T> >&, const std::vector<Modular<T> >&) [with T = std::integral_constant<long long int, 75161927681>]'
  808 |         c[i + j] += a[i] * b[j];
      |                     ~~~~~^~~~
a.cc:843:18:   required from here
  843 |   auto res = a * a;
      |                  ^
a.cc:436:3: error: no type named 'type' in 'struct std::enable_if<false, Modular<std::integral_constant<long long int, 75161927681> > >'
  436 |   operator*=(const Modular &rhs) {
      |   ^~~~~~~~
a.cc: In instantiation of 'Modular<T> operator*(const Modular<T>&, const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]':
a.cc:808:26:   required from 'std::vector<Modular<T> > operator*(const std::vector<Modular<T> >&, const std::vector<Modular<T> >&) [with T = std::integral_constant<long long int, 75161927681>]'
  808 |         c[i + j] += a[i] * b[j];
      |                     ~~~~~^~~~
a.cc:843:18:   required from here
  843 |   auto res = a * a;
      |                  ^
a.cc:446:3: note: candidate: 'template<class U> typename std::enable_if<(! std::is_integral<typename Modular<U>::Type>::value), Modular<T> >::type& Modular<T>::operator*=(const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]'
  446 |   operator*=(const Modular &rhs) {
      |   ^~~~~~~~
a.cc:446:3: note:   template argument deduction/substitution failed:
a.cc: In substitution of 'template<class U> typename std::enable_if<(! std::is_integral<typename Modular<T>::Type>::value), Modular<std::integral_constant<long long int, 75161927681> > >::type& Modular<std::integral_constant<long long int, 75161927681> >::operator*=(const Modular<std::integral_constant<long long int, 75161927681> >&) [with U = std::integral_constant<long long int, 75161927681>]':
a.cc:535:26:   required from 'Modular<T> operator*(const Modular<T>&, const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]'
  535 |   return Modular<T>(lhs) *= rhs;
      |          ~~~~~~~~~~~~~~~~^~~~~~
a.cc:808:26:   required from 'std::vector<Modular<T> > operator*(const std::vector<Modular<T> >&, const std::vector<Modular<T> >&) [with T = std::integral_constant<long long int, 75161927681>]'
  808 |         c[i + j] += a[i] * b[j];
      |                     ~~~~~^~~~
a.cc:843:18:   required from here
  843 |   auto res = a * a;
      |                  ^
a.cc:446:3: error: no type named 'type' in 'struct std::enable_if<false, Modular<std::integral_constant<long long int, 75161927681> > >'
  446 |   operator*=(const Modular &rhs) {
      |   ^~~~~~~~
a.cc: In instantiation of 'Modular<T> operator*(const Modular<T>&, const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]':
a.cc:808:26:   required from 'std::vector<Modular<T> > operator*(const std::vector<Modular<T> >&, const std::vector<Modular<T> >&) [with T = std::integral_constant<long long int, 75161927681>]'
  808 |         c[i + j] += a[i] * b[j];
      |                     ~~~~~^~~~
a.cc:843:18:   required from here
  843 |   auto res = a * a;
      |                  ^
a.cc:816:26: note: candidate: 'template<class T> std::vector<Modular<T> >& operator*=(std::vector<Modular<T> >&, const std::vector<Modular<T> >&)'
  816 | std::vector<Modular<T>> &operator*=(std::vector<Modular<T>> &a,
      |                          ^~~~~~~~
a.cc:816:26: note:   template argument deduction/substitution failed:
a.cc:535:26: note:   'Modular<std::integral_constant<long long int, 75161927681> >' is not derived from 'std::vector<Modular<T> >'
  535 |   return Modular<T>(lhs) *= rhs;
      |          ~~~~~~~~~~~~~~~~^~~~~~
a.cc: In instantiation of 'static std::vector<Modular<T> > NTT<T>::multiply(std::vector<Modular<T> >, std::vector<Modular<T> >) [with T = std::integral_constant<long long int, 75161927681>]':
a.cc:813:26:   required from 'std::vector<Modular<T> > operator*(const std::vector<Modular<T> >&, const std::vector<Modular<T> >&) [with T = std::integral_constant<long long int, 75161927681>]'
  813 |   return NTT<T>::multiply(a, b);
      |          ~~~~~~~~~~~~~~~~^~~~~~
a.cc:843:18:   required from here
  843 |   auto res = a * a;
      |                  ^
a.cc:719:12: error: no match for 'operator*=' (operand types are '__gnu_cxx::__alloc_traits<std::allocator<Modular<std::integral_constant<long long int, 75161927681> > >, Modular<std::integral_constant<long long int, 75161927681> > >::value_type' {aka 'Modular<std::integral_constant<long long int, 75161927681> >'} and 'Modular<std::integral_constant<long long int, 75161927681> >')
  719 |       a[i] *= b[i] * inv_sz;
      |       ~~~~~^~~~~~~~~~~~~~~~
a.cc:419:3: note: candidate: 'template<class U> typename std::enable_if<std::is_same<typename Modular<U>::Type, int>::value, Modular<T> >::type& Modular<T>::operator*=(const Modular<T>&) [with T = std::integral_constant<long long int, 75161927681>]'
  419 |   operator*=(const Modular &rhs) {
      |   ^~~~~~~~
a.cc:419:3: note:   template argument deduction/substitution failed:
a.cc: In substitution of 'template<class U> typename std::enable_if<std::is_same<typename Modular<T>::Type, int>::value, Modular<std::integral_constant<long long int, 75161927681> > >::type& Modular<std::integral_constant<long long int, 75161927681> >::operator*=(const Modular<std::integral_constant<long long int, 75161927681> >&) [with U = std::integral_constant<long long int, 75161927681>]':
a.cc:719:12:   required from 'static std::vector<Modular<T> > NTT<T>::multiply(std::vector<Modular<T> >, std::vector<Modular<T> >) [with T = std::integral_constant<long long int, 75161927681>]'
  719 |       a[i] *= b[i] * inv_sz;
      |       ~~~~~^~~~~~~~~~~~~~~~
a.cc:813:26:   required from 'std::vector<Modular<T> > operator*(const std::vector<Modular<T> >&, const std::vector<Modular<T> >&) [with T = std::integral_constant<long long int, 75161927681>]'
  813 |   return NTT<T>::multiply(a, b);
      |          ~~~~~~~~~~~~~~~~^~~~~~
a.cc:843:18:   required from here
  843 |   auto res = a * a;
      |                  ^
a.cc:419:3: error: no type named 'type' in 'struct std::enable_if<false, Modular<std::integral_constant<long long int, 75161927681> > >'
  419 |   operator*=(const Modular &rhs) {
      |   ^~~~~~~~
a.cc: In insta