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;
using ll = long long;
using ull = unsigned long long;
template <class T>
using vec = vector<T>;
template <class T>
using vvec = vector<vec<T>>;
constexpr long long INF = 1LL << 60;
constexpr int INF_INT = 1 << 25;
constexpr long long MOD = 998244353LL;
using ld = long double;
static const ld pi = 3.141592653589793L;
template <class T>
inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
struct Edge {
  ll to, rev;
  long double cap;
  Edge(ll _to, long double _cap, ll _rev) {
    to = _to;
    cap = _cap;
    rev = _rev;
  }
};
using Edges = vector<Edge>;
using Graph = vector<Edges>;
void add_edge(Graph &G, ll from, ll to, long double cap, bool revFlag,
              long double revCap) {
  G[from].push_back(Edge(to, cap, (ll)G[to].size()));
  if (revFlag) G[to].push_back(Edge(from, revCap, (ll)G[from].size() - 1));
}
template <int mod>
struct NumberTheoreticTransform {
  vector<int> rev, rts;
  int base, max_base, root;
  NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} {
    assert(mod >= 3 && mod % 2 == 1);
    auto tmp = mod - 1;
    max_base = 0;
    while (tmp % 2 == 0) tmp >>= 1, max_base++;
    root = 2;
    while (mod_pow(root, (mod - 1) >> 1) == 1) ++root;
    assert(mod_pow(root, mod - 1) == 1);
    root = mod_pow(root, (mod - 1) >> max_base);
  }
  inline int mod_pow(int x, int n) {
    int ret = 1;
    while (n > 0) {
      if (n & 1) ret = mul(ret, x);
      x = mul(x, x);
      n >>= 1;
    }
    return ret;
  }
  inline int inverse(int x) { return mod_pow(x, mod - 2); }
  inline unsigned add(unsigned x, unsigned y) {
    x += y;
    if (x >= mod) x -= mod;
    return x;
  }
  inline unsigned mul(unsigned a, unsigned b) {
    return 1ull * a * b % (unsigned long long)mod;
  }
  void ensure_base(int nbase) {
    if (nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for (int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    assert(nbase <= max_base);
    while (base < nbase) {
      int z = mod_pow(root, 1 << (max_base - 1 - base));
      for (int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        rts[(i << 1) + 1] = mul(rts[i], z);
      }
      ++base;
    }
  }
  void ntt(vector<int> &a) {
    const int n = (int)a.size();
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for (int i = 0; i < n; i++) {
      if (i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for (int k = 1; k < n; k <<= 1) {
      for (int i = 0; i < n; i += 2 * k) {
        for (int j = 0; j < k; j++) {
          int z = mul(a[i + j + k], rts[j + k]);
          a[i + j + k] = add(a[i + j], mod - z);
          a[i + j] = add(a[i + j], z);
        }
      }
    }
  }
  vector<int> multiply(vector<int> a, vector<int> b) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while ((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    a.resize(sz, 0);
    b.resize(sz, 0);
    ntt(a);
    ntt(b);
    int inv_sz = inverse(sz);
    for (int i = 0; i < sz; i++) {
      a[i] = mul(a[i], mul(b[i], inv_sz));
    }
    reverse(a.begin() + 1, a.end());
    ntt(a);
    a.resize(need);
    return a;
  }
  vector<int> pow(vector<int> a, int k) {
    if (k <= 1) return a;
    if (k & 1)
      return multiply(a, pow(a, k - 1));
    else
      return pow(multiply(a, a), k / 2);
  }
};
NumberTheoreticTransform<MOD> ntt;
void solve() {
  int n, k;
  cin >> n >> k;
  vec<int> d(k);
  vec<int> a(10, 0);
  for (int(i) = (int)(0); i < (int)(k); ++i) {
    cin >> d[i];
    a[d[i]] = 1;
  }
  a = ntt.pow(a, n / 2);
  int ans = 0;
  for (auto i : a) {
    ans = ntt.add(ans, ntt.mul(i, i));
  }
  cout << ans << '\n';
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  solve();
  return 0;
}