#include <bits/stdc++.h>

#include <algorithm>
#include <array>

#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

#include <utility>

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

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

#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

#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

#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

using i64 = long long;
using u64 = unsigned long long;
#define REP(i, n) for (int i = 0, REP_N_ = int(n); i < REP_N_; ++i)
#define ALL(x) std::begin(x), std::end(x)

template <class T>
inline bool chmax(T &a, T b) {
  return a < b and ((a = std::move(b)), true);
}
template <class T>
inline bool chmin(T &a, T b) {
  return a > b and ((a = std::move(b)), true);
}

template <typename T>
using V = std::vector<T>;
template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &a) {
  for (auto &x : a) is >> x;
  return is;
}
template <typename Container>
std::ostream &pprint(const Container &a, std::string_view sep = " ",
                     std::string_view ends = "\n", std::ostream *os = nullptr) {
  if (os == nullptr) os = &std::cout;
  auto b = std::begin(a), e = std::end(a);
  for (auto it = std::begin(a); it != e; ++it) {
    if (it != b) *os << sep;
    *os << *it;
  }
  return *os << ends;
}
template <typename T, typename = void>
struct is_iterable : std::false_type {};
template <typename T>
struct is_iterable<T, std::void_t<decltype(std::begin(std::declval<T>())),
                                  decltype(std::end(std::declval<T>()))>>
    : std::true_type {};

template <typename T,
          typename = std::enable_if_t<is_iterable<T>::value &&
                                      !std::is_same<T, std::string>::value>>
std::ostream &operator<<(std::ostream &os, const T &a) {
  return pprint(a, ", ", "", &(os << "{")) << "}";
}
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &a) {
  return os << "(" << a.first << ", " << a.second << ")";
}

#ifdef ENABLE_DEBUG
template <typename T>
void pdebug(const T &value) {
  std::cerr << value;
}
template <typename T, typename... Ts>
void pdebug(const T &value, const Ts &... args) {
  pdebug(value);
  std::cerr << ", ";
  pdebug(args...);
}
#define DEBUG(...)                                   \
  do {                                               \
    std::cerr << " \033[33m (L" << __LINE__ << ") "; \
    std::cerr << #__VA_ARGS__ << ":\033[0m ";        \
    pdebug(__VA_ARGS__);                             \
    std::cerr << std::endl;                          \
  } while (0)
#else
#define pdebug(...)
#define DEBUG(...)
#endif

using namespace std;

// Formal Power Series (dense format).
template <typename T, int DMAX>
struct DenseFPS {
  // Coefficients of terms from x^0 to x^DMAX.
  std::vector<T> coeff_;

  DenseFPS() : coeff_(DMAX + 1) {}  // zero-initialized
  explicit DenseFPS(std::vector<T> c) : coeff_(std::move(c)) {
    assert((int)coeff_.size() == DMAX + 1);
  }

  DenseFPS(const DenseFPS &other) : coeff_(other.coeff_) {}
  DenseFPS(DenseFPS &&other) : coeff_(std::move(other.coeff_)) {}
  DenseFPS &operator=(const DenseFPS &other) {
    coeff_ = other.coeff_;
    return *this;
  }
  DenseFPS &operator=(DenseFPS &&other) {
    coeff_ = std::move(other.coeff_);
    return *this;
  }

  static constexpr int size() { return DMAX + 1; }

  // Returns the coefficient of x^d.
  const T &operator[](int d) const { return coeff_[d]; }

  DenseFPS &operator+=(const T &scalar) {
    coeff_[0] += scalar;
    return *this;
  }
  friend DenseFPS operator+(const DenseFPS &x, const T &scalar) {
    DenseFPS res = x;
    res += scalar;
    return res;
  }
  DenseFPS &operator+=(const DenseFPS &other) {
    for (int i = 0; i < size(); ++i) coeff_[i] += other[i];
    return *this;
  }
  friend DenseFPS operator+(const DenseFPS &x, const DenseFPS &y) {
    DenseFPS res = x;
    res += y;
    return res;
  }

  DenseFPS &operator-=(const DenseFPS &other) {
    for (int i = 0; i < size(); ++i) coeff_[i] -= other[i];
    return *this;
  }
  friend DenseFPS operator-(const DenseFPS &x, const DenseFPS &y) {
    DenseFPS res = x;
    res -= y;
    return res;
  }

  DenseFPS &operator*=(const T &scalar) {
    for (auto &x : coeff_) x *= scalar;
    return *this;
  }
  friend DenseFPS operator*(const DenseFPS &x, const T &scalar) {
    DenseFPS res = x;
    res *= scalar;
    return res;
  }
  DenseFPS &operator*=(const DenseFPS &other) {
    *this = this->mul_naive(other);
    return *this;
  }
  friend DenseFPS operator*(const DenseFPS &x, const DenseFPS &y) {
    return x.mul_naive(y);
  }

 private:
  // Naive multiplication. O(N^2)
  DenseFPS mul_naive(const DenseFPS &other) const {
    DenseFPS res;
    for (int i = 0; i < size(); ++i) {
      for (int j = 0; i + j < size(); ++j) {
        res.coeff_[i + j] += (*this)[i] * other[j];
      }
    }
    return res;
  }
};

namespace fps {

// Fast polynomial multiplication by single NTT.
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> mul_ntt(const DenseFPS<ModInt, DMAX> &x,
                               const DenseFPS<ModInt, DMAX> &y) {
  static_assert(ModInt::mod() != 1'000'000'007);  // Must be a NTT-friendly MOD!
  auto z = atcoder::convolution(x.coeff_, y.coeff_);
  z.resize(DMAX + 1);  // Maybe shrink.
  return DenseFPS<ModInt, DMAX>(std::move(z));
}

// Polynomial multiplication by NTT + Garner (arbitrary mod).
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> mul_mod(const DenseFPS<ModInt, DMAX> &x,
                               const DenseFPS<ModInt, DMAX> &y) {
  std::vector<i64> xll(x.size()), yll(y.size());
  for (int i = 0; i < x.size(); ++i) {
    xll[i] = x[i].val();
  }
  for (int i = 0; i < y.size(); ++i) {
    yll[i] = y[i].val();
  }
  auto zll = atcoder::convolution_ll(xll, yll);
  DenseFPS<ModInt, DMAX> res;
  int n = std::min<int>(res.size(), zll.size());
  for (int i = 0; i < n; ++i) {
    res.coeff_[i] = zll[i];
  }
  return res;
}

// Polynomial multiplication by NTT + Garner (long long).
template <int DMAX>
DenseFPS<i64, DMAX> mul_ll(const DenseFPS<i64, DMAX> &x,
                           const DenseFPS<i64, DMAX> &y) {
  auto z = atcoder::convolution_ll(x.coeff_, y.coeff_);
  z.resize(DMAX + 1);  // Maybe shrink.
  return DenseFPS<i64, DMAX>(std::move(z));
}

template <typename T, int DMAX, typename Func>
DenseFPS<T, DMAX> pow_generic(const DenseFPS<T, DMAX> &x, u64 t, Func mulfunc) {
  DenseFPS<T, DMAX> base = x, res;
  res.coeff_[0] = 1;
  while (t) {
    if (t & 1) res = mulfunc(res, base);
    base = mulfunc(base, base);
    t >>= 1;
  }
  return res;
}

template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> pow_ntt(const DenseFPS<ModInt, DMAX> &x, u64 t) {
  return pow_generic(x, t, mul_ntt);
}

template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> pow_mod(const DenseFPS<ModInt, DMAX> &x, u64 t) {
  return pow_generic(x, t, mul_mod);
}

template <int DMAX>
DenseFPS<i64, DMAX> pow_ll(const DenseFPS<i64, DMAX> &x, u64 t) {
  return pow_generic(x, t, mul_ll);
}

}  // namespace fps

// Formal Power Series (sparse format).
template <typename T>
struct SparseFPS {
  int size_;
  std::vector<int> degree_;
  std::vector<T> coeff_;

  SparseFPS() : size_(0) {}

  explicit SparseFPS(std::vector<std::pair<int, T>> terms)
      : size_(terms.size()), degree_(size_), coeff_(size_) {
    // Sort by degree_ in ascending order.
    sort(terms.begin(), terms.end());
    for (int i = 0; i < size_; ++i) {
      degree_[i] = terms[i].first;
      coeff_[i] = terms[i].second;
    }
  }

  inline int size() const { return size_; }
  inline int degree(int i) const { return degree_[i]; }
  inline const T &coeff(int i) const { return coeff_[i]; }

  int DMAX() const { return (size_ == 0) ? 0 : degree_.back(); }

  void emplace_back(int d, T c) {
    if (not degree_.empty()) {
      assert(d > degree_.back());
    }
    degree_.push_back(std::move(d));
    coeff_.push_back(std::move(c));
    ++size_;
  }

  // Returns the coefficient of x^d.
  T operator[](int d) const {
    auto it = std::lower_bound(degree_.begin(), degree_.end(), d);
    if (it == degree_.end() or *it != d) return (T)(0);
    int j = std::distance(degree_.begin(), it);
    return coeff_[j];
  }

  SparseFPS &operator+=(const T &scalar) {
    for (auto &x : coeff_) x += scalar;
    return *this;
  }
  friend SparseFPS operator+(const SparseFPS &x, const T &scalar) {
    SparseFPS res = x;
    res += scalar;
    return res;
  }
  SparseFPS &operator+=(const SparseFPS &other) {
    *this = this->add(other);
    return *this;
  }
  friend SparseFPS operator+(const SparseFPS &x, const SparseFPS &y) {
    return x.add(y);
  }

  SparseFPS &operator*=(const T &scalar) {
    for (auto &x : coeff_) x *= scalar;
    return *this;
  }
  friend SparseFPS operator*(const SparseFPS &x, const T &scalar) {
    SparseFPS res = x;
    res *= scalar;
    return res;
  }

  SparseFPS &operator-=(const SparseFPS &other) {
    *this = this->add(other * -1);
    return *this;
  }
  friend SparseFPS operator-(const SparseFPS &x, const SparseFPS &y) {
    return x.add(y * -1);
  }

  SparseFPS mul(const SparseFPS &other, int max_degree) const {
    std::map<int, T> terms;
    for (int i = 0; i < size(); ++i) {
      int di = degree(i);
      T ci = coeff(i);
      for (int j = 0; j < other.size(); ++j) {
        int dj = other.degree(j);
        if (di + dj > max_degree) break;
        terms[di + dj] += ci * other.coeff(j);
      }
    }
    SparseFPS res;
    for (auto &[d, c] : terms) {
      res.emplace_back(d, c);
    }
    return res;
  }

 private:
  SparseFPS add(const SparseFPS &other) const {
    SparseFPS res;
    int j = 0;
    for (int i = 0; i < size();) {
      const int deg = this->degree(i);
      for (; j < other.size() and other.degree(j) < deg; ++j) {
        res.emplace_back(other.degree(j), other.coeff(j));
      }
      T c = this->coeff(i);
      if (j < other.size() and other.degree(j) == deg) {
        c += other.coeff(j);
        ++j;
      }
      if (c != 0) {
        res.emplace_back(deg, c);
      }
    }
    for (; j < other.size(); ++j) {
      res.emplace_back(other.degree(j), other.coeff(j));
    }
    return res;
  }
};

// Polynomial addition (dense + sparse).
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> &operator+=(DenseFPS<ModInt, DMAX> &x,
                                   const SparseFPS<ModInt> &y) {
  for (int i = 0; i < y.size(); ++i) {
    if (y.degree(i) > DMAX) break;  // ignore
    x.coeff_[y.degree(i)] += y.coeff(i);
  }
  return x;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator+(const DenseFPS<ModInt, DMAX> &x,
                                 const SparseFPS<ModInt> &y) {
  DenseFPS<ModInt, DMAX> res = x;
  res += y;
  return res;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator+(const SparseFPS<ModInt> &x,
                                 const DenseFPS<ModInt, DMAX> &y) {
  return y + x;  // commutative
}

// Polynomial multiplication (dense * sparse).
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> &operator*=(DenseFPS<ModInt, DMAX> &x,
                                   const SparseFPS<ModInt> &y) {
  if (y.size() == 0) {
    return x *= 0;
  }
  ModInt c0 = 0;
  int j0 = 0;
  if (y.degree(0) == 0) {
    c0 = y.coeff(0);
    ++j0;
  }
  for (int i = DMAX; i >= 0; --i) {
    x.coeff_[i] *= c0;
    for (int j = j0; j < y.size(); ++j) {
      int d = y.degree(j);
      if (d > i) break;
      x.coeff_[i] += x[i - d] * y.coeff(j);
    }
  }
  return x;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator*(const DenseFPS<ModInt, DMAX> &x,
                                 const SparseFPS<ModInt> &y) {
  DenseFPS<ModInt, DMAX> res = x;
  res *= y;
  return res;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator*(const SparseFPS<ModInt> &x,
                                 const DenseFPS<ModInt, DMAX> &y) {
  return y * x;  // commutative
}

// Polynomial division (dense / sparse).
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> &operator/=(DenseFPS<ModInt, DMAX> &x,
                                   const SparseFPS<ModInt> &y) {
  assert(y.size() > 0 and y.degree(0) == 0 and y.coeff(0) != 0);
  ModInt inv_c0 = y.coeff(0).inv();
  for (int i = 0; i < x.size(); ++i) {
    for (int j = 1; j < y.size(); ++j) {
      int d = y.degree(j);
      if (d > i) break;
      x.coeff_[i] -= x.coeff_[i - d] * y.coeff[j];
    }
    x.coeff_[i] *= inv_c0;
  }
  return x;
}
template <typename ModInt, int DMAX>
DenseFPS<ModInt, DMAX> operator/(const DenseFPS<ModInt, DMAX> &x,
                                 const SparseFPS<ModInt> &y) {
  DenseFPS<ModInt, DMAX> res = x;
  res /= y;
  return res;
}

using mint = atcoder::modint998244353;
const int MOD = 998244353;
const int BMAX = 200'000;

template <class T>
struct Factorials {
  // factorials and inverse factorials.
  std::vector<T> fact, ifact;

  // n: max cached value.
  Factorials(size_t n) : fact(n + 1), ifact(n + 1) {
    assert(n > 0 and n < MOD);
    fact[0] = 1;
    for (size_t i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (size_t i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i;
  }

  // Combination (nCk)
  T C(int n, int k) {
    if (k < 0 || k > n) return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }

  // Permutation (nPk)
  T P(int n, int k) {
    if (k < 0 || k > n) return 0;
    return fact[n] * ifact[n - k];
  }
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  int N, Q;
  cin >> N >> Q;
  V<int> A(N);
  cin >> A;

  deque<SparseFPS<mint>> q;
  REP(i, N) {
    SparseFPS<mint> g;
    g.emplace_back(0, mint(A[i] - 1));
    g.emplace_back(1, mint(1));
    q.push_back(move(g));
  }
  deque<DenseFPS<mint, BMAX>> qd;
  while (q.size() > 1) {
    SparseFPS<mint> p = q[0].mul(q[1], BMAX);
    q.pop_front();
    q.pop_front();
    if (p.size() < 1000) {
      q.push_back(move(p));
    } else {
      DenseFPS<mint, BMAX> d;
      REP(i, p.size()) { d.coeff_[p.degree(i)] = p.coeff(i); }
      qd.push_back(move(d));
    }
  }
  if (q.size() == 1) {
    SparseFPS<mint> p = q.front();
    DenseFPS<mint, BMAX> d;
    REP(i, p.size()) { d.coeff_[p.degree(i)] = p.coeff(i); }
    qd.push_back(move(d));
  }
  while (qd.size() > 1) {
    DenseFPS<mint, BMAX> p = fps::mul_ntt(qd[0], qd[1]);
    qd.pop_front();
    qd.pop_front();
    qd.push_back(move(p));
  }
  const auto &f = qd.front();

  REP(i, Q) {
    int b;
    cin >> b;
    cout << f[b].val() << '\n';
  }
}