結果

問題 No.1939 Numbered Colorful Balls
ユーザー noshi91noshi91
提出日時 2022-05-13 22:38:32
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 146 ms / 2,000 ms
コード長 23,089 bytes
コンパイル時間 3,286 ms
コンパイル使用メモリ 228,572 KB
実行使用メモリ 9,600 KB
最終ジャッジ日時 2023-09-29 08:09:49
合計ジャッジ時間 6,749 ms
ジャッジサーバーID
(参考情報)
judge11 / judge14
このコードへのチャレンジ(β)

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 146 ms
9,552 KB
testcase_01 AC 2 ms
4,376 KB
testcase_02 AC 146 ms
9,520 KB
testcase_03 AC 146 ms
9,492 KB
testcase_04 AC 2 ms
4,376 KB
testcase_05 AC 146 ms
9,600 KB
testcase_06 AC 146 ms
9,456 KB
testcase_07 AC 34 ms
4,620 KB
testcase_08 AC 16 ms
4,376 KB
testcase_09 AC 142 ms
8,776 KB
testcase_10 AC 3 ms
4,376 KB
testcase_11 AC 70 ms
6,168 KB
testcase_12 AC 10 ms
4,380 KB
testcase_13 AC 3 ms
4,380 KB
testcase_14 AC 33 ms
4,656 KB
testcase_15 AC 18 ms
4,380 KB
testcase_16 AC 73 ms
6,864 KB
testcase_17 AC 69 ms
6,268 KB
testcase_18 AC 34 ms
4,876 KB
testcase_19 AC 139 ms
8,724 KB
testcase_20 AC 33 ms
4,640 KB
testcase_21 AC 140 ms
8,944 KB
testcase_22 AC 9 ms
4,376 KB
testcase_23 AC 70 ms
6,408 KB
testcase_24 AC 140 ms
9,104 KB
testcase_25 AC 69 ms
6,400 KB
testcase_26 AC 145 ms
9,500 KB
testcase_27 AC 2 ms
4,376 KB
testcase_28 AC 2 ms
4,376 KB
testcase_29 AC 72 ms
6,424 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

#include <bits/stdc++.h>

#pragma GCC target("popcnt")

#include <array>
#include <cstddef>

#ifndef __GNUC__

int __builtin_ctz(const unsigned int c) noexcept {
  static constexpr std::array<std::uint8_t, 32> table = {
      0,  1, 2,  6,  3,  11, 7,  16, 4,  14, 12, 21, 8,  23, 17, 26,
      31, 5, 10, 15, 13, 20, 22, 25, 30, 9,  19, 24, 29, 18, 28, 27 };
  return table[(c & ~c + 1) * 0x4653ADF >> 27 & 0x1F];
}

int __builtin_ctzll(const unsigned long long c) noexcept {
  static constexpr std::array<std::uint8_t, 64> table = {
      0,  1,  2,  7,  3,  13, 8,  27, 4,  33, 14, 36, 9,  49, 28, 19,
      5,  25, 34, 17, 15, 53, 37, 55, 10, 46, 50, 39, 29, 42, 20, 57,
      63, 6,  12, 26, 32, 35, 48, 18, 24, 16, 52, 54, 45, 38, 41, 56,
      62, 11, 31, 47, 23, 51, 44, 40, 61, 30, 22, 43, 60, 21, 59, 58 };
  return table[(c & ~c + 1) * 0x218A7A392DD9ABFULL >> 58 & 0x3F];
}

int __builtin_clz(unsigned int c) noexcept {
  static constexpr std::array<std::uint8_t, 32> table = {
      0,  1, 2,  6,  3,  11, 7,  16, 4,  14, 12, 21, 8,  23, 17, 26,
      31, 5, 10, 15, 13, 20, 22, 25, 30, 9,  19, 24, 29, 18, 28, 27 };
  c |= c >> 1;
  c |= c >> 2;
  c |= c >> 4;
  c |= c >> 8;
  c |= c >> 16;
  return table[((c >> 1) + 1) * 0x4653ADF >> 27 & 0x1F];
}

int __builtin_clzll(unsigned long long c) noexcept {
  static constexpr std::array<std::uint8_t, 64> table = {
      0,  1,  2,  7,  3,  13, 8,  27, 4,  33, 14, 36, 9,  49, 28, 19,
      5,  25, 34, 17, 15, 53, 37, 55, 10, 46, 50, 39, 29, 42, 20, 57,
      63, 6,  12, 26, 32, 35, 48, 18, 24, 16, 52, 54, 45, 38, 41, 56,
      62, 11, 31, 47, 23, 51, 44, 40, 61, 30, 22, 43, 60, 21, 59, 58 };
  c |= c >> 1;
  c |= c >> 2;
  c |= c >> 4;
  c |= c >> 8;
  c |= c >> 16;
  c |= c >> 32;
  return table[((c >> 1) + 1) * 0x218A7A392DD9ABFULL >> 58 & 0x3F];
}

constexpr int __builtin_popcount(unsigned int c) noexcept {
  c -= c >> 1 & 0x55555555;
  c = (c & 0x33333333) + (c >> 2 & 0x33333333);
  c = (c + (c >> 4)) & 0x0F0F0F0F;
  return c * 0x01010101 >> 24 & 0x3F;
}

constexpr int __builtin_popcountll(unsigned long long c) noexcept {
  c -= c >> 1 & 0x5555555555555555;
  c = (c & 0x3333333333333333) + (c >> 2 & 0x3333333333333333);
  c = (c + (c >> 4)) & 0x0F0F0F0F0F0F0F0F;
  return c * 0x0101010101010101 >> 56 & 0x7f;
}

constexpr bool __builtin_parity(unsigned int c) noexcept {
  c ^= c >> 1;
  c ^= c >> 2;
  return ((c & 0x11111111) * 0x11111111 >> 28 & 0x1) != 0;
}

constexpr bool __builtin_parityll(unsigned long long c) noexcept {
  c ^= c >> 1;
  c ^= c >> 2;
  return ((c & 0x1111111111111111) * 0x1111111111111111 >> 60 & 0x1) != 0;
}

#endif

using namespace std;

// https://ei1333.github.io/library/test/verify/yosupo-inv-of-formal-power-series.test.cpp

// #line 1 "test/verify/yosupo-inv-of-formal-power-series.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/inv_of_formal_power_series"

// #line 1 "template/template.cpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
  for (T& in : v)
    is >> in;
  return is;
}

template <typename T1, typename T2> inline bool chmax(T1& a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2> inline bool chmin(T1& a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64> vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T& t, const V& v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T& t, const V& v) {
  for (auto& e : t)
    fill_v(e, v);
}

template <typename F> struct FixPoint : F {
  explicit FixPoint(F&& f) : F(forward<F>(f)) {}

  template <typename... Args> decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F> inline decltype(auto) MFP(F&& f) {
  return FixPoint<F>{forward<F>(f)};
}
// #line 4 "test/verify/yosupo-inv-of-formal-power-series.test.cpp"

// #line 1 "math/combinatorics/mod-int.cpp"
template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt& operator+=(const ModInt& p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt& operator-=(const ModInt& p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt& operator*=(const ModInt& p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt& operator/=(const ModInt& p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt& p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt& p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt& p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt& p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt& p) const { return x == p.x; }

  bool operator!=(const ModInt& p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream& operator<<(ostream& os, const ModInt& p) { return os << p.x; }

  friend istream& operator>>(istream& is, ModInt& a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt<mod>;
// #line 1 "math/fft/number-theoretic-transform-friendly-mod-int.cpp"
/**
 * @brief Number Theoretic Transform Friendly ModInt
 */
template <typename Mint> struct NumberTheoreticTransformFriendlyModInt {

  static vector<Mint> roots, iroots, rate3, irate3;
  static int max_base;

  NumberTheoreticTransformFriendlyModInt() = default;

  static void init() {
    if (roots.empty()) {
      const unsigned mod = Mint::get_mod();
      assert(mod >= 3 && mod % 2 == 1);
      auto tmp = mod - 1;
      max_base = 0;
      while (tmp % 2 == 0)
        tmp >>= 1, max_base++;
      Mint root = 2;
      while (root.pow((mod - 1) >> 1) == 1) {
        root += 1;
      }
      assert(root.pow(mod - 1) == 1);

      roots.resize(max_base + 1);
      iroots.resize(max_base + 1);
      rate3.resize(max_base + 1);
      irate3.resize(max_base + 1);

      roots[max_base] = root.pow((mod - 1) >> max_base);
      iroots[max_base] = Mint(1) / roots[max_base];
      for (int i = max_base - 1; i >= 0; i--) {
        roots[i] = roots[i + 1] * roots[i + 1];
        iroots[i] = iroots[i + 1] * iroots[i + 1];
      }
      {
        Mint prod = 1, iprod = 1;
        for (int i = 0; i <= max_base - 3; i++) {
          rate3[i] = roots[i + 3] * prod;
          irate3[i] = iroots[i + 3] * iprod;
          prod *= iroots[i + 3];
          iprod *= roots[i + 3];
        }
      }
    }
  }

  static void ntt(vector<Mint>& a) {
    init();
    const int n = (int)a.size();
    assert((n & (n - 1)) == 0);
    int h = __builtin_ctz(n);
    assert(h <= max_base);
    int len = 0;
    Mint imag = roots[2];
    if (h & 1) {
      int p = 1 << (h - 1);
      Mint rot = 1;
      for (int i = 0; i < p; i++) {
        auto r = a[i + p];
        a[i + p] = a[i] - r;
        a[i] += r;
      }
      len++;
    }
    for (; len + 1 < h; len += 2) {
      int p = 1 << (h - len - 2);
      { // s = 0
        for (int i = 0; i < p; i++) {
          auto a0 = a[i];
          auto a1 = a[i + p];
          auto a2 = a[i + 2 * p];
          auto a3 = a[i + 3 * p];
          auto a1na3imag = (a1 - a3) * imag;
          auto a0a2 = a0 + a2;
          auto a1a3 = a1 + a3;
          auto a0na2 = a0 - a2;
          a[i] = a0a2 + a1a3;
          a[i + 1 * p] = a0a2 - a1a3;
          a[i + 2 * p] = a0na2 + a1na3imag;
          a[i + 3 * p] = a0na2 - a1na3imag;
        }
      }
      Mint rot = rate3[0];
      for (int s = 1; s < (1 << len); s++) {
        int offset = s << (h - len);
        Mint rot2 = rot * rot;
        Mint rot3 = rot2 * rot;
        for (int i = 0; i < p; i++) {
          auto a0 = a[i + offset];
          auto a1 = a[i + offset + p] * rot;
          auto a2 = a[i + offset + 2 * p] * rot2;
          auto a3 = a[i + offset + 3 * p] * rot3;
          auto a1na3imag = (a1 - a3) * imag;
          auto a0a2 = a0 + a2;
          auto a1a3 = a1 + a3;
          auto a0na2 = a0 - a2;
          a[i + offset] = a0a2 + a1a3;
          a[i + offset + 1 * p] = a0a2 - a1a3;
          a[i + offset + 2 * p] = a0na2 + a1na3imag;
          a[i + offset + 3 * p] = a0na2 - a1na3imag;
        }
        rot *= rate3[__builtin_ctz(~s)];
      }
    }
  }

  static void intt(vector<Mint>& a, bool f = true) {
    init();
    const int n = (int)a.size();
    assert((n & (n - 1)) == 0);
    int h = __builtin_ctz(n);
    assert(h <= max_base);
    int len = h;
    Mint iimag = iroots[2];
    for (; len > 1; len -= 2) {
      int p = 1 << (h - len);
      { // s = 0
        for (int i = 0; i < p; i++) {
          auto a0 = a[i];
          auto a1 = a[i + 1 * p];
          auto a2 = a[i + 2 * p];
          auto a3 = a[i + 3 * p];
          auto a2na3iimag = (a2 - a3) * iimag;
          auto a0na1 = a0 - a1;
          auto a0a1 = a0 + a1;
          auto a2a3 = a2 + a3;
          a[i] = a0a1 + a2a3;
          a[i + 1 * p] = (a0na1 + a2na3iimag);
          a[i + 2 * p] = (a0a1 - a2a3);
          a[i + 3 * p] = (a0na1 - a2na3iimag);
        }
      }
      Mint irot = irate3[0];
      for (int s = 1; s < (1 << (len - 2)); s++) {
        int offset = s << (h - len + 2);
        Mint irot2 = irot * irot;
        Mint irot3 = irot2 * irot;
        for (int i = 0; i < p; i++) {
          auto a0 = a[i + offset];
          auto a1 = a[i + offset + 1 * p];
          auto a2 = a[i + offset + 2 * p];
          auto a3 = a[i + offset + 3 * p];
          auto a2na3iimag = (a2 - a3) * iimag;
          auto a0na1 = a0 - a1;
          auto a0a1 = a0 + a1;
          auto a2a3 = a2 + a3;
          a[i + offset] = a0a1 + a2a3;
          a[i + offset + 1 * p] = (a0na1 + a2na3iimag) * irot;
          a[i + offset + 2 * p] = (a0a1 - a2a3) * irot2;
          a[i + offset + 3 * p] = (a0na1 - a2na3iimag) * irot3;
        }
        irot *= irate3[__builtin_ctz(~s)];
      }
    }
    if (len >= 1) {
      int p = 1 << (h - 1);
      for (int i = 0; i < p; i++) {
        auto ajp = a[i] - a[i + p];
        a[i] += a[i + p];
        a[i + p] = ajp;
      }
    }
    if (f) {
      Mint inv_sz = Mint(1) / n;
      for (int i = 0; i < n; i++)
        a[i] *= inv_sz;
    }
  }

  static vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while ((1 << nbase) < need)
      nbase++;
    int sz = 1 << nbase;
    a.resize(sz, 0);
    b.resize(sz, 0);
    ntt(a);
    ntt(b);
    Mint inv_sz = Mint(1) / sz;
    for (int i = 0; i < sz; i++)
      a[i] *= b[i] * inv_sz;
    intt(a, false);
    a.resize(need);
    return a;
  }
};

template <typename Mint>
vector<Mint>
NumberTheoreticTransformFriendlyModInt<Mint>::roots = vector<Mint>();
template <typename Mint>
vector<Mint>
NumberTheoreticTransformFriendlyModInt<Mint>::iroots = vector<Mint>();
template <typename Mint>
vector<Mint>
NumberTheoreticTransformFriendlyModInt<Mint>::rate3 = vector<Mint>();
template <typename Mint>
vector<Mint>
NumberTheoreticTransformFriendlyModInt<Mint>::irate3 = vector<Mint>();
template <typename Mint>
int NumberTheoreticTransformFriendlyModInt<Mint>::max_base = 0;
// #line 2 "math/fps/formal-power-series-friendly-ntt.cpp"

/**
 * @brief Formal Power Series Friendly NTT(NTTmod用形式的冪級数)
 * @docs docs/formal-power-series-friendly-ntt.md
 */
template <typename T> struct FormalPowerSeriesFriendlyNTT : vector<T> {
  using vector<T>::vector;
  using P = FormalPowerSeriesFriendlyNTT;
  using NTT = NumberTheoreticTransformFriendlyModInt<T>;

  P pre(int deg) const {
    return P(begin(*this), begin(*this) + min((int)this->size(), deg));
  }

  P rev(int deg = -1) const {
    P ret(*this);
    if (deg != -1)
      ret.resize(deg, T(0));
    reverse(begin(ret), end(ret));
    return ret;
  }

  void shrink() {
    while (this->size() && this->back() == T(0))
      this->pop_back();
  }

  P operator+(const P& r) const { return P(*this) += r; }

  P operator+(const T& v) const { return P(*this) += v; }

  P operator-(const P& r) const { return P(*this) -= r; }

  P operator-(const T& v) const { return P(*this) -= v; }

  P operator*(const P& r) const { return P(*this) *= r; }

  P operator*(const T& v) const { return P(*this) *= v; }

  P operator/(const P& r) const { return P(*this) /= r; }

  P operator%(const P& r) const { return P(*this) %= r; }

  P& operator+=(const P& r) {
    if (r.size() > this->size())
      this->resize(r.size());
    for (int i = 0; i < (int)r.size(); i++)
      (*this)[i] += r[i];
    return *this;
  }

  P& operator-=(const P& r) {
    if (r.size() > this->size())
      this->resize(r.size());
    for (int i = 0; i < (int)r.size(); i++)
      (*this)[i] -= r[i];
    return *this;
  }

  // https://judge.yosupo.jp/problem/convolution_mod
  P& operator*=(const P& r) {
    if (this->empty() || r.empty()) {
      this->clear();
      return *this;
    }
    auto ret = NTT::multiply(*this, r);
    return *this = { begin(ret), end(ret) };
  }

  P& operator/=(const P& r) {
    if (this->size() < r.size()) {
      this->clear();
      return *this;
    }
    int n = this->size() - r.size() + 1;
    return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
  }

  P& operator%=(const P& r) {
    *this -= *this / r * r;
    shrink();
    return *this;
  }

  // https://judge.yosupo.jp/problem/division_of_polynomials
  pair<P, P> div_mod(const P& r) {
    P q = *this / r;
    P x = *this - q * r;
    x.shrink();
    return make_pair(q, x);
  }

  P operator-() const {
    P ret(this->size());
    for (int i = 0; i < (int)this->size(); i++)
      ret[i] = -(*this)[i];
    return ret;
  }

  P& operator+=(const T& r) {
    if (this->empty())
      this->resize(1);
    (*this)[0] += r;
    return *this;
  }

  P& operator-=(const T& r) {
    if (this->empty())
      this->resize(1);
    (*this)[0] -= r;
    return *this;
  }

  P& operator*=(const T& v) {
    for (int i = 0; i < (int)this->size(); i++)
      (*this)[i] *= v;
    return *this;
  }

  P dot(P r) const {
    P ret(min(this->size(), r.size()));
    for (int i = 0; i < (int)ret.size(); i++)
      ret[i] = (*this)[i] * r[i];
    return ret;
  }

  P operator>>(int sz) const {
    if ((int)this->size() <= sz)
      return {};
    P ret(*this);
    ret.erase(ret.begin(), ret.begin() + sz);
    return ret;
  }

  P operator<<(int sz) const {
    P ret(*this);
    ret.insert(ret.begin(), sz, T(0));
    return ret;
  }

  T operator()(T x) const {
    T r = 0, w = 1;
    for (auto& v : *this) {
      r += w * v;
      w *= x;
    }
    return r;
  }

  P diff() const {
    const int n = (int)this->size();
    P ret(max(0, n - 1));
    for (int i = 1; i < n; i++)
      ret[i - 1] = (*this)[i] * T(i);
    return ret;
  }

  P integral() const {
    const int n = (int)this->size();
    P ret(n + 1);
    ret[0] = T(0);
    for (int i = 0; i < n; i++)
      ret[i + 1] = (*this)[i] / T(i + 1);
    return ret;
  }

  // https://judge.yosupo.jp/problem/inv_of_formal_power_series
  // F(0) must not be 0
  P inv(int deg = -1) const {
    assert(((*this)[0]) != T(0));
    const int n = (int)this->size();
    if (deg == -1)
      deg = n;
    P res(deg);
    res[0] = { T(1) / (*this)[0] };
    for (int d = 1; d < deg; d <<= 1) {
      P f(2 * d), g(2 * d);
      for (int j = 0; j < min(n, 2 * d); j++)
        f[j] = (*this)[j];
      for (int j = 0; j < d; j++)
        g[j] = res[j];
      NTT::ntt(f);
      NTT::ntt(g);
      f = f.dot(g);
      NTT::intt(f);
      for (int j = 0; j < d; j++)
        f[j] = 0;
      NTT::ntt(f);
      for (int j = 0; j < 2 * d; j++)
        f[j] *= g[j];
      NTT::intt(f);
      for (int j = d; j < min(2 * d, deg); j++)
        res[j] = -f[j];
    }
    return res;
  }

  // https://judge.yosupo.jp/problem/log_of_formal_power_series
  // F(0) must be 1
  P log(int deg = -1) const {
    assert((*this)[0] == T(1));
    const int n = (int)this->size();
    if (deg == -1)
      deg = n;
    return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
  }

  // https://judge.yosupo.jp/problem/sqrt_of_formal_power_series
  P sqrt(int deg = -1,
    const function<T(T)>& get_sqrt = [](T) { return T(1); }) const {
    const int n = (int)this->size();
    if (deg == -1)
      deg = n;
    if ((*this)[0] == T(0)) {
      for (int i = 1; i < n; i++) {
        if ((*this)[i] != T(0)) {
          if (i & 1)
            return {};
          if (deg - i / 2 <= 0)
            break;
          auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);
          if (ret.empty())
            return {};
          ret = ret << (i / 2);
          if ((int)ret.size() < deg)
            ret.resize(deg, T(0));
          return ret;
        }
      }
      return P(deg, 0);
    }
    auto sqr = T(get_sqrt((*this)[0]));
    if (sqr * sqr != (*this)[0])
      return {};
    P ret{ sqr };
    T inv2 = T(1) / T(2);
    for (int i = 1; i < deg; i <<= 1) {
      ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
    }
    return ret.pre(deg);
  }

  P sqrt(const function<T(T)>& get_sqrt, int deg = -1) const {
    return sqrt(deg, get_sqrt);
  }

  // https://judge.yosupo.jp/problem/exp_of_formal_power_series
  // F(0) must be 0
  P exp(int deg = -1) const {
    if (deg == -1)
      deg = this->size();
    assert((*this)[0] == T(0));

    P inv;
    inv.reserve(deg + 1);
    inv.push_back(T(0));
    inv.push_back(T(1));

    auto inplace_integral = [&](P& F) -> void {
      const int n = (int)F.size();
      auto mod = T::get_mod();
      while ((int)inv.size() <= n) {
        int i = inv.size();
        inv.push_back((-inv[mod % i]) * (mod / i));
      }
      F.insert(begin(F), T(0));
      for (int i = 1; i <= n; i++)
        F[i] *= inv[i];
    };

    auto inplace_diff = [](P& F) -> void {
      if (F.empty())
        return;
      F.erase(begin(F));
      T coeff = 1, one = 1;
      for (int i = 0; i < (int)F.size(); i++) {
        F[i] *= coeff;
        coeff += one;
      }
    };

    P b{ 1, 1 < (int)this->size() ? (*this)[1] : 0 }, c{ 1 }, z1, z2{ 1, 1 };
    for (int m = 2; m < deg; m *= 2) {
      auto y = b;
      y.resize(2 * m);
      NTT::ntt(y);
      z1 = z2;
      P z(m);
      for (int i = 0; i < m; ++i)
        z[i] = y[i] * z1[i];
      NTT::intt(z);
      fill(begin(z), begin(z) + m / 2, T(0));
      NTT::ntt(z);
      for (int i = 0; i < m; ++i)
        z[i] *= -z1[i];
      NTT::intt(z);
      c.insert(end(c), begin(z) + m / 2, end(z));
      z2 = c;
      z2.resize(2 * m);
      NTT::ntt(z2);
      P x(begin(*this), begin(*this) + min<int>(this->size(), m));
      inplace_diff(x);
      x.push_back(T(0));
      NTT::ntt(x);
      for (int i = 0; i < m; ++i)
        x[i] *= y[i];
      NTT::intt(x);
      x -= b.diff();
      x.resize(2 * m);
      for (int i = 0; i < m - 1; ++i)
        x[m + i] = x[i], x[i] = T(0);
      NTT::ntt(x);
      for (int i = 0; i < 2 * m; ++i)
        x[i] *= z2[i];
      NTT::intt(x);
      x.pop_back();
      inplace_integral(x);
      for (int i = m; i < min<int>(this->size(), 2 * m); ++i)
        x[i] += (*this)[i];
      fill(begin(x), begin(x) + m, T(0));
      NTT::ntt(x);
      for (int i = 0; i < 2 * m; ++i)
        x[i] *= y[i];
      NTT::intt(x);
      b.insert(end(b), begin(x) + m, end(x));
    }
    return P{ begin(b), begin(b) + deg };
  }

  // https://judge.yosupo.jp/problem/pow_of_formal_power_series
  P pow(int64_t k, int deg = -1) const {
    const int n = (int)this->size();
    if (deg == -1)
      deg = n;
    for (int i = 0; i < n; i++) {
      if ((*this)[i] != T(0)) {
        T rev = T(1) / (*this)[i];
        P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
        if (i * k > deg)
          return P(deg, T(0));
        ret = (ret << (i * k)).pre(deg);
        if ((int)ret.size() < deg)
          ret.resize(deg, T(0));
        return ret;
      }
    }
    return *this;
  }

  P mod_pow(int64_t k, P g) const {
    P modinv = g.rev().inv();
    auto get_div = [&](P base) {
      if (base.size() < g.size()) {
        base.clear();
        return base;
      }
      int n = base.size() - g.size() + 1;
      return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
    };
    P x(*this), ret{ 1 };
    while (k > 0) {
      if (k & 1) {
        ret *= x;
        ret -= get_div(ret) * g;
        ret.shrink();
      }
      x *= x;
      x -= get_div(x) * g;
      x.shrink();
      k >>= 1;
    }
    return ret;
  }

  // https://judge.yosupo.jp/problem/polynomial_taylor_shift
  P taylor_shift(T c) const {
    int n = (int)this->size();
    vector<T> fact(n), rfact(n);
    fact[0] = rfact[0] = T(1);
    for (int i = 1; i < n; i++)
      fact[i] = fact[i - 1] * T(i);
    rfact[n - 1] = T(1) / fact[n - 1];
    for (int i = n - 1; i > 1; i--)
      rfact[i - 1] = rfact[i] * T(i);
    P p(*this);
    for (int i = 0; i < n; i++)
      p[i] *= fact[i];
    p = p.rev();
    P bs(n, T(1));
    for (int i = 1; i < n; i++)
      bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];
    p = (p * bs).pre(n);
    p = p.rev();
    for (int i = 0; i < n; i++)
      p[i] *= rfact[i];
    return p;
  }
};

template <typename Mint> using FPS = FormalPowerSeriesFriendlyNTT<Mint>;
// #line 7 "test/verify/yosupo-inv-of-formal-power-series.test.cpp"

const int MOD = 998244353;
using mint = ModInt<MOD>;

int main() {
  int N, M;
  cin >> N >> M;
  FPS<mint> G(N + 1, 0);
  G[0] = 1;
  for (int i = 0; i < M; i++) {
    int l;
    cin >> l;
    G[l] = 1;
  }

  cout << G.pow(N + 1)[N] / (N + 1) << "\n";

  return 0;
}
0