Problem: All bus tickets in Berland have their numbers. A number consists of n digits (n is even). Only k decimal digits d_1, d_2, ..., d_k can be used to form ticket numbers. If 0 is among these digits, then numbers may have leading zeroes. For example, if n = 4 and only digits 0 and 4 can be used, then 0000, 4004, 4440 are valid ticket numbers, and 0002, 00, 44443 are not.

A ticket is lucky if the sum of first n / 2 digits is equal to the sum of remaining n / 2 digits. 

Calculate the number of different lucky tickets in Berland. Since the answer may be big, print it modulo 998244353.

Input

The first line contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 10) — the number of digits in each ticket number, and the number of different decimal digits that may be used. n is even.

The second line contains a sequence of pairwise distinct integers d_1, d_2, ..., d_k (0 ≤ d_i ≤ 9) — the digits that may be used in ticket numbers. The digits are given in arbitrary order.

Output

Print the number of lucky ticket numbers, taken modulo 998244353.

Examples

Input

4 2
1 8


Output

6


Input

20 1
6


Output

1


Input

10 5
6 1 4 0 3


Output

569725


Input

1000 7
5 4 0 1 8 3 2


Output

460571165

Note

In the first example there are 6 lucky ticket numbers: 1111, 1818, 1881, 8118, 8181 and 8888.

There is only one ticket number in the second example, it consists of 20 digits 6. This ticket number is lucky, so the answer is 1.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  os << '{';
  string sep;
  for (const auto &x : v) os << sep << x, sep = ", ";
  return os << '}';
}
template <typename A, typename B>
ostream &operator<<(ostream &os, const pair<A, B> &p) {
  return os << '(' << p.first << ", " << p.second << ')';
}
void dbg_out() { cerr << endl; }
template <typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) {
  cerr << ' ' << H;
  dbg_out(T...);
}
template <const int &MOD>
struct _m_int {
  int val;
  _m_int(int64_t v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = v;
  }
  static int mod_inv(int a, int m = MOD) {
    int g = m, r = a, x = 0, y = 1;
    while (r != 0) {
      int q = g / r;
      g %= r;
      swap(g, r);
      x -= q * y;
      swap(x, y);
    }
    return x < 0 ? x + m : x;
  }
  explicit operator int() const { return val; }
  explicit operator int64_t() const { return val; }
  _m_int &operator+=(const _m_int &other) {
    val -= MOD - other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  _m_int &operator-=(const _m_int &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return x % m;
    unsigned x_high = x >> 32, x_low = (unsigned)x;
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  _m_int &operator*=(const _m_int &other) {
    val = fast_mod((uint64_t)val * other.val);
    return *this;
  }
  _m_int &operator/=(const _m_int &other) { return *this *= other.inv(); }
  friend _m_int operator+(const _m_int &a, const _m_int &b) {
    return _m_int(a) += b;
  }
  friend _m_int operator-(const _m_int &a, const _m_int &b) {
    return _m_int(a) -= b;
  }
  friend _m_int operator*(const _m_int &a, const _m_int &b) {
    return _m_int(a) *= b;
  }
  friend _m_int operator/(const _m_int &a, const _m_int &b) {
    return _m_int(a) /= b;
  }
  _m_int &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  _m_int &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  _m_int operator++(int) {
    _m_int before = *this;
    ++*this;
    return before;
  }
  _m_int operator--(int) {
    _m_int before = *this;
    --*this;
    return before;
  }
  _m_int operator-() const { return val == 0 ? 0 : MOD - val; }
  bool operator==(const _m_int &other) const { return val == other.val; }
  bool operator!=(const _m_int &other) const { return val != other.val; }
  _m_int inv() const { return mod_inv(val); }
  _m_int pow(int64_t p) const {
    if (p < 0) return inv().pow(-p);
    _m_int a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      a *= a;
      p >>= 1;
    }
    return result;
  }
  friend ostream &operator<<(ostream &os, const _m_int &m) {
    return os << m.val;
  }
};
extern const int MOD = 998244353;
using mod_int = _m_int<MOD>;
template <const int &MOD>
struct NTT {
  using ntt_int = _m_int<MOD>;
  vector<ntt_int> roots = {0, 1};
  vector<int> bit_reverse;
  int max_size = -1;
  ntt_int root;
  void reset() {
    roots = {0, 1};
    max_size = -1;
  }
  static bool is_power_of_two(int n) { return (n & (n - 1)) == 0; }
  static int round_up_power_two(int n) {
    while (n & (n - 1)) n = (n | (n - 1)) + 1;
    return max(n, 1);
  }
  static int get_length(int n) {
    assert(is_power_of_two(n));
    return __builtin_ctz(n);
  }
  void bit_reorder(int n, vector<ntt_int> &values) {
    if ((int)bit_reverse.size() != n) {
      bit_reverse.assign(n, 0);
      int length = get_length(n);
      for (int i = 1; i < n; i++)
        bit_reverse[i] = (bit_reverse[i >> 1] >> 1) | ((i & 1) << (length - 1));
    }
    for (int i = 0; i < n; i++)
      if (i < bit_reverse[i]) swap(values[i], values[bit_reverse[i]]);
  }
  void find_root() {
    max_size = 1 << __builtin_ctz(MOD - 1);
    root = 2;
    while (!(root.pow(max_size) == 1 && root.pow(max_size / 2) != 1)) root++;
  }
  void prepare_roots(int n) {
    if (max_size < 0) find_root();
    assert(n <= max_size);
    if ((int)roots.size() >= n) return;
    int length = get_length(roots.size());
    roots.resize(n);
    while (1 << length < n) {
      ntt_int z = root.pow(max_size >> (length + 1));
      for (int i = 1 << (length - 1); i < 1 << length; i++) {
        roots[2 * i] = roots[i];
        roots[2 * i + 1] = roots[i] * z;
      }
      length++;
    }
  }
  void fft_iterative(int N, vector<ntt_int> &values) {
    assert(is_power_of_two(N));
    prepare_roots(N);
    bit_reorder(N, values);
    for (int n = 1; n < N; n *= 2)
      for (int start = 0; start < N; start += 2 * n)
        for (int i = 0; i < n; i++) {
          ntt_int even = values[start + i];
          ntt_int odd = values[start + n + i] * roots[n + i];
          values[start + n + i] = even - odd;
          values[start + i] = even + odd;
        }
  }
  void invert_fft(int N, vector<ntt_int> &values) {
    ntt_int inv_N = ntt_int(N).inv();
    for (int i = 0; i < N; i++) values[i] *= inv_N;
    reverse(values.begin() + 1, values.end());
    fft_iterative(N, values);
  }
  const int FFT_CUTOFF = 150;
  template <typename T>
  vector<T> mod_multiply(const vector<T> &_left, const vector<T> &_right,
                         bool circular = false) {
    if (_left.empty() || _right.empty()) return {};
    vector<ntt_int> left(_left.begin(), _left.end());
    vector<ntt_int> right(_right.begin(), _right.end());
    int n = left.size();
    int m = right.size();
    int output_size = circular ? round_up_power_two(max(n, m)) : n + m - 1;
    if (min(n, m) < FFT_CUTOFF) {
      auto &&mod_output_size = [&](int x) {
        return x < output_size ? x : x - output_size;
      };
      static const uint64_t U64_BOUND =
          numeric_limits<uint64_t>::max() - (uint64_t)MOD * MOD;
      vector<uint64_t> result(output_size, 0);
      for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) {
          int index = mod_output_size(i + j);
          result[index] += (uint64_t)(int64_t)left[i] * (int64_t)right[j];
          if (result[index] > U64_BOUND) result[index] %= MOD;
        }
      for (uint64_t &x : result)
        if (x >= MOD) x %= MOD;
      return vector<T>(result.begin(), result.end());
    }
    int N = round_up_power_two(output_size);
    left.resize(N, 0);
    right.resize(N, 0);
    if (left == right) {
      fft_iterative(N, left);
      right = left;
    } else {
      fft_iterative(N, left);
      fft_iterative(N, right);
    }
    for (int i = 0; i < N; i++) left[i] *= right[i];
    invert_fft(N, left);
    return vector<T>(left.begin(), left.begin() + output_size);
  }
  template <typename T>
  vector<T> mod_power(const vector<T> &v, int exponent) {
    assert(exponent >= 0);
    vector<T> result = {1};
    if (exponent == 0) return result;
    for (int k = 31 - __builtin_clz(exponent); k >= 0; k--) {
      result = mod_multiply(result, result);
      if (exponent >> k & 1) result = mod_multiply(result, v);
    }
    return result;
  }
  template <typename T>
  vector<T> mod_multiply_all(const vector<vector<T>> &polynomials) {
    if (polynomials.empty()) return {1};
    struct compare_size {
      bool operator()(const vector<T> &x, const vector<T> &y) {
        return x.size() > y.size();
      }
    };
    priority_queue<vector<T>, vector<vector<T>>, compare_size> pq(
        polynomials.begin(), polynomials.end());
    while (pq.size() > 1) {
      vector<T> a = pq.top();
      pq.pop();
      vector<T> b = pq.top();
      pq.pop();
      pq.push(mod_multiply(a, b));
    }
    return pq.top();
  }
};
NTT<MOD> ntt;
auto random_address = [] {
  char *p = new char;
  delete p;
  return (uint64_t)p;
};
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count() *
               (random_address() | 1));
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n, k, x;
  cin >> n >> k;
  vector<mod_int> A(10, 0);
  for (int i = 0; i < k; i++) {
    cin >> x;
    A[x] = 1;
  }
  A = ntt.mod_power(A, n / 2);
  mod_int res = 0;
  for (auto x : A) {
    res += x * x;
  }
  cout << res;
}