#define MOD_TYPE 1

#pragma region Macros

#include <bits/stdc++.h>
using namespace std;

#if 0
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using Int = boost::multiprecision::cpp_int;
using lld = boost::multiprecision::cpp_dec_float_100;
#endif
#if 1
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pld = pair<ld, ld>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;

constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353);
constexpr int INF = (int)1e9 + 10;
constexpr ll LINF = (ll)4e18;
constexpr double PI = acos(-1.0);
constexpr double EPS = 1e-7;
constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0};
constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0};

#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define REPI(i, m, n) for (int i = m; i < (int)(n); ++i)
#define repi(i, n) REPI(i, 0, n)
#define MP make_pair
#define MT make_tuple
#define YES(n) cout << ((n) ? "YES" : "NO") << "\n"
#define Yes(n) cout << ((n) ? "Yes" : "No") << "\n"
#define possible(n) cout << ((n) ? "possible" : "impossible") << "\n"
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n"
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << "\n";

struct io_init
{
  io_init()
  {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(30) << setiosflags(ios::fixed);
  };
} io_init;
template <typename T>
inline bool chmin(T &a, T b)
{
  if (a > b)
  {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
inline bool chmax(T &a, T b)
{
  if (a < b)
  {
    a = b;
    return true;
  }
  return false;
}
inline ll CEIL(ll a, ll b)
{
  return (a + b - 1) / b;
}
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T &val)
{
  fill((T *)array, (T *)(array + N), val);
}
template <typename T, typename U>
constexpr istream &operator>>(istream &is, pair<T, U> &p) noexcept
{
  is >> p.first >> p.second;
  return is;
}
template <typename T, typename U>
constexpr ostream &operator<<(ostream &os, pair<T, U> &p) noexcept
{
  os << p.first << " " << p.second;
  return os;
}
#pragma endregion

// internal_bit
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

// internal_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

// internal_math
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 modular multiplication 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 < 2^31`
      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;
      constexpr long long bases[3] = {2, 7, 61};
      for (long long a : bases)
      {
        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

// modint
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

// convolution
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

#pragma region mint
template <int MOD>
struct Fp
{
  long long val;

  constexpr Fp(long long v = 0) noexcept : val(v % MOD)
  {
    if (val < 0)
      v += MOD;
  }

  constexpr int getmod()
  {
    return MOD;
  }

  constexpr Fp operator-() const noexcept
  {
    return val ? MOD - val : 0;
  }

  constexpr Fp operator+(const Fp &r) const noexcept
  {
    return Fp(*this) += r;
  }

  constexpr Fp operator-(const Fp &r) const noexcept
  {
    return Fp(*this) -= r;
  }

  constexpr Fp operator*(const Fp &r) const noexcept
  {
    return Fp(*this) *= r;
  }

  constexpr Fp operator/(const Fp &r) const noexcept
  {
    return Fp(*this) /= r;
  }

  constexpr Fp &operator+=(const Fp &r) noexcept
  {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }

  constexpr Fp &operator-=(const Fp &r) noexcept
  {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }

  constexpr Fp &operator*=(const Fp &r) noexcept
  {
    val = val * r.val % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }

  constexpr Fp &operator/=(const Fp &r) noexcept
  {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b)
    {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }

  constexpr bool operator==(const Fp &r) const noexcept
  {
    return this->val == r.val;
  }

  constexpr bool operator!=(const Fp &r) const noexcept
  {
    return this->val != r.val;
  }

  friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept
  {
    return os << x.val;
  }

  friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) noexcept
  {
    return is >> x.val;
  }
};

Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept
{
  if (n == 0)
    return 1;
  auto t = modpow(a, n / 2);
  t = t * t;
  if (n & 1)
    t = t * a;
  return t;
}

using mint = Fp<MOD>;
#pragma endregion

void solve()
{
  int n;
  cin >> n;
  vector<ll> a(n + 1), b(n + 1);
  rep(i, n + 1) cin >> a[i];
  rep(i, n + 1) cin >> b[i];
  auto c = atcoder::convolution<MOD>(a, b);
  mint sum = 0;
  rep(i, n + 1) sum += c[i];
  cout << sum << "\n";
}

int main()
{
  solve();
}