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>
static const int MOD = 1000000007;
using ll = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using namespace std;
template <class T>
constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;
constexpr int ntt_mod = 998244353, ntt_root = 3;
template <u32 M = 1000000007>
struct modint {
  u32 val;
  modint() : val(0) {}
  template <typename T>
  modint(T t) {
    t %= (T)M;
    if (t < 0) t += (T)M;
    val = t;
  }
  modint pow(ll k) const {
    modint res(1), x(val);
    while (k) {
      if (k & 1) res *= x;
      x *= x;
      k >>= 1;
    }
    return res;
  }
  template <typename T>
  modint& operator=(T t) {
    t %= (T)M;
    if (t < 0) t += (T)M;
    val = t;
    return *this;
  }
  modint inv() const { return pow(M - 2); }
  modint& operator+=(modint a) {
    val += a.val;
    if (val >= M) val -= M;
    return *this;
  }
  modint& operator-=(modint a) {
    if (val < a.val)
      val += M - a.val;
    else
      val -= a.val;
    return *this;
  }
  modint& operator*=(modint a) {
    val = (u64)val * a.val % M;
    return *this;
  }
  modint& operator/=(modint a) { return (*this) *= a.inv(); }
  modint operator+(modint a) const { return modint(val) += a; }
  modint operator-(modint a) const { return modint(val) -= a; }
  modint operator*(modint a) const { return modint(val) *= a; }
  modint operator/(modint a) const { return modint(val) /= a; }
  modint operator-() { return modint(M - val); }
  bool operator==(const modint a) const { return val == a.val; }
  bool operator!=(const modint a) const { return val != a.val; }
  bool operator<(const modint a) const { return val < a.val; }
};
using mint = modint<ntt_mod>;
class NTT {
  static constexpr int max_base = 21, maxN = 1 << max_base;
  mint roots[maxN << 1], iroots[maxN << 1];

 public:
  NTT() {
    for (int i = 0; i <= max_base; ++i) {
      const int offset = (1 << i) - 1;
      const mint g = mint(ntt_root).pow((ntt_mod) / (1 << i)), ginv = g.inv();
      mint x = 1, y = 1;
      for (int j = 0; j < 1 << i; ++j) {
        roots[offset + j] = x;
        x *= g;
        iroots[offset + j] = y;
        y *= ginv;
      }
    }
  }
  void transform(vector<mint>& a, int sign) {
    const int n = a.size();
    if (!sign) {
      for (int k = n >> 1; k >= 1; k >>= 1) {
        for (int i = 0; i < n; i += k << 1) {
          for (int j = 0; j < k; ++j) {
            const mint tmp = a[i + j] - a[i + j + k];
            a[i + j] += a[i + j + k];
            a[i + j + k] = tmp * roots[(k << 1) - 1 + j];
          }
        }
      }
    } else {
      for (int k = 1; k <= (n >> 1); k <<= 1) {
        for (int i = 0; i < n; i += k << 1) {
          for (int j = 0; j < k; ++j) {
            a[i + j + k] *= iroots[(k << 1) - 1 + j];
            const mint tmp = a[i + j] - a[i + j + k];
            a[i + j] += a[i + j + k];
            a[i + j + k] = tmp;
          }
        }
      }
      const mint x = mint(n).inv();
      for (auto&& i : a) i *= x;
    }
  }
};
NTT ntt;
struct poly {
  vector<mint> v;
  poly() = default;
  explicit poly(int n) : v(n){};
  explicit poly(vector<mint> vv) : v(std::move(vv)){};
  int size() const { return (int)v.size(); }
  poly cut(int len) {
    if (len < v.size()) v.resize(static_cast<unsigned long>(len));
    return *this;
  }
  inline mint& operator[](int i) { return v[i]; }
  poly& operator+=(const poly& a) {
    this->v.resize(max(size(), a.size()));
    for (int i = 0; i < a.size(); ++i) this->v[i] += a.v[i];
    return *this;
  }
  poly& operator-=(const poly& a) {
    this->v.resize(max(size(), a.size()));
    for (int i = 0; i < a.size(); ++i) this->v[i] -= a.v[i];
    return *this;
  }
  poly& operator*=(poly a) {
    int N = size() + a.size() - 1;
    int sz = 1;
    while (sz < N) sz <<= 1;
    this->v.resize(sz);
    a.v.resize(sz);
    ntt.transform(this->v, 0);
    ntt.transform(a.v, 0);
    for (int i = 0; i < sz; ++i) this->v[i] *= a.v[i];
    ntt.transform(this->v, 1);
    this->v.resize(N);
    return *this;
  }
  poly& operator/=(const poly& a) { return (*this *= a.inv()); }
  poly operator+(const poly& a) const { return poly(*this) += a; }
  poly operator-(const poly& a) const { return poly(*this) -= a; }
  poly operator*(const poly& a) const { return poly(*this) *= a; }
  poly inv() const {
    int n = size();
    poly r(1);
    r[0] = (this->v[0]).inv();
    int k = 1;
    while (k < n) {
      k *= 2;
      poly ff(k);
      for (int i = 0; i < min(k, n); ++i) {
        ff[i] = this->v[i];
      }
      poly nr = (r * r * ff).cut(k);
      for (int i = 0; i < k / 2; ++i) {
        nr[i] = (r[i] + r[i] - nr[i]);
        nr[i + k / 2] = -nr[i + k / 2];
      }
      r = nr;
    }
    r.v.resize(n);
    return r;
  }
};
template <class T>
T pow_(T x, T n, T M) {
  uint64_t u = 1, xx = x;
  while (n > 0) {
    if (n & 1) u = u * xx % M;
    xx = xx * xx % M;
    n >>= 1;
  }
  return static_cast<T>(u);
};
int main() {
  int n, k;
  cin >> n >> k;
  n /= 2;
  vector<int> v(k);
  for (auto&& i : v) scanf("%d", &i);
  auto f = poly(*max_element(v.begin(), v.end()) + 1);
  for (int i = 0; i < k; ++i) {
    f[v[i]] += mint(1);
  }
  auto g = poly(1);
  g[0] = mint(1);
  while (n > 0) {
    if (n & 1) g *= f;
    f *= f;
    n >>= 1;
  }
  mint ans = 0;
  for (int i = 0; i < g.size(); ++i) {
    ans += g[i] * g[i];
  }
  cout << ans.val << "\n";
  return 0;
}