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>
#pragma GCC optimize("O3")
using namespace std;
const long double pi = acos(-1.0);
const long double log23 = 1.58496250072115618145373894394781;
const long double eps = 1e-8;
const long long INF = 1e18 + 239;
const long long prost = 239;
const int two = 2;
const int th = 3;
const int BIG = 1e9 + 239;
const int alf = 26;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, 1, 0, -1};
const int dxb[4] = {-1, 1, 1, -1};
const int dyb[4] = {-1, 1, -1, 1};
const int dxo[8] = {-1, -1, -1, 0, 1, 1, 1, 0};
const int dyo[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
const int dig = 10;
const int day[12] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int digarr[10] = {6, 2, 5, 5, 4, 5, 6, 3, 7, 6};
const long long bt = 30;
template <typename T>
inline T gcd(T a, T b) {
  while (a) {
    b %= a;
    swap(a, b);
  }
  return b;
}
template <typename T>
inline T lcm(T a, T b) {
  return (a / gcd(a, b)) * b;
}
inline bool is_down(char x) { return ('a' <= x && x <= 'z'); }
inline bool is_upper(char x) { return ('A' <= x && x <= 'Z'); }
inline bool is_digit(char x) { return ('0' <= x && x <= '9'); }
mt19937_64 rnd(239);
const int M = 2e5 + 239;
const int N = (2 * M);
const int L = 18;
const int T = (1 << 21);
const int B = trunc(sqrt(M)) + 1;
const int X = 110;
const int MOD = 998244353;
const long long MOD2 = MOD * MOD;
const long long root = 3;
const long long sub = 15311432;
const long long sub_inv = 469870224;
int st[T], rev[T];
int p_fft, w_fft, z_fft, s_fft, k_fft;
inline int power(int a, long long n) {
  int ans = 1;
  while (n) {
    if (n & 1LL) ans = 1LL * ans * a % MOD;
    a = 1LL * a * a % MOD;
    n >>= 1LL;
  }
  return ans;
}
inline int inv(int x) { return power(x, MOD - 2); }
inline void fft(vector<int> &a) {
  for (int i = 0; i < s_fft; i++)
    if (i < rev[i]) swap(a[i], a[rev[i]]);
  for (int k = 1; k < s_fft; k <<= 1)
    for (int i = 0; i < s_fft; i += k + k)
      for (int j = i, t = i + k; j < i + k; j++, t++) {
        z_fft = 1LL * a[t] * st[t - i] % MOD;
        a[t] = a[j] - z_fft;
        if (a[t] < 0) a[t] += MOD;
        a[j] = a[j] + z_fft;
        if (a[j] >= MOD) a[j] -= MOD;
      }
}
inline vector<int> multiply(vector<int> a, vector<int> b) {
  k_fft = ((int)a.size() + (int)b.size()) - 1;
  p_fft = 0;
  while ((1 << p_fft) < k_fft) p_fft++;
  s_fft = (1 << p_fft);
  for (int i = 0; i < s_fft; i++)
    rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (p_fft - 1));
  st[0] = 0;
  st[1] = 1;
  for (int b = 1; b < p_fft; b++) {
    w_fft = power(sub, 1 << (22 - b));
    for (int i = (1 << (b - 1)); i < (1 << b); i++) {
      st[i << 1] = st[i];
      st[(i << 1) + 1] = 1LL * st[i] * w_fft % MOD;
    }
  }
  while (a.size() < s_fft) a.push_back(0);
  while (b.size() < s_fft) b.push_back(0);
  fft(a);
  fft(b);
  for (int b = 1; b < p_fft; b++) {
    w_fft = power(sub_inv, 1 << (22 - b));
    for (int i = (1 << (b - 1)); i < (1 << b); i++) {
      st[i << 1] = st[i];
      st[(i << 1) + 1] = 1LL * st[i] * w_fft % MOD;
    }
  }
  vector<int> v;
  for (int i = 0; i < s_fft; i++) v.push_back(1LL * a[i] * b[i] % MOD);
  fft(v);
  while (v.back() == 0) v.pop_back();
  k_fft = inv(s_fft);
  for (int i = 0; i < (int)v.size(); i++) v[i] = 1LL * k_fft * v[i] % MOD;
  return v;
}
struct poly : vector<int> {
  poly(const vector<int> &a) : vector<int>(a) {}
  poly(int n) : vector<int>(n, 1) {}
  inline void normalize() {
    while (size() > 1 && back() == 0) pop_back();
  }
  inline int &operator[](int pos) {
    if (pos >= (int)size()) resize(pos + 1);
    return vector<int>::operator[](pos);
  }
  inline int operator[](int pos) const {
    if (pos < (int)size()) return vector<int>::operator[](pos);
    return 0;
  }
  inline poly operator+(const poly &b) const {
    const poly &a = *this;
    poly ans(max((int)a.size(), (int)b.size()));
    for (int i = 0; i < ans.size(); i++) {
      ans[i] = (a[i] + b[i]);
      if (ans[i] >= MOD) ans[i] -= MOD;
    }
    return ans;
  }
  inline poly operator+=(const poly &p) { return *this = *this + p; }
  inline poly operator-(const poly &b) const {
    const poly &a = *this;
    poly ans(max((int)a.size(), (int)b.size()));
    for (int i = 0; i < ans.size(); i++) {
      ans[i] = (a[i] - b[i]);
      if (ans[i] < 0) ans[i] += MOD;
    }
    return ans;
  }
  inline poly operator-=(const poly &p) { return *this = *this - p; }
  inline poly operator*(int d) const {
    poly ans = *this;
    for (int i = 0; i < (int)ans.size(); i++) ans[i] = (1LL * ans[i] * d % MOD);
    return ans;
  }
  inline poly operator*=(int d) { return *this = *this * d; }
  inline poly operator/(int d) const {
    d = inv(d);
    poly ans = *this;
    for (int i = 0; i < (int)ans.size(); i++) ans[i] = (1LL * ans[i] * d % MOD);
    return ans;
  }
  inline poly operator/=(int d) { return *this = *this / d; }
  inline poly operator*(const poly &p) const {
    return poly(multiply(*this, p));
  }
  inline poly operator*=(const poly &p) { return *this = *this * p; }
  inline poly cut(int n) const {
    poly a = (*this);
    a.resize(n);
    return a;
  }
  inline poly invp() const {
    poly a(1);
    if ((*this)[0] != 1) a[0] = inv((*this)[0]);
    for (int n = 1; n < (int)size(); n <<= 1) {
      poly ca = cut(n + n);
      poly ra = (a * a);
      ra.cut(n + n);
      ra = (ra * ca);
      ra.cut(n + n);
      a += a;
      a -= ra;
      a = a.cut(n + n);
    }
    a.resize(size());
    return a;
  }
  inline poly rev() const {
    poly a = (*this);
    reverse(a.begin(), a.end());
    return a;
  }
  inline poly getdiv(poly b) const {
    poly a = (*this);
    a.normalize();
    b.normalize();
    if (a.size() < b.size()) return poly({0});
    int k = (int)a.size() - (int)b.size() + 1;
    if (b.back() != 1) b /= b.back();
    poly rb = b.rev().cut(k);
    return (rb.invp() * a.rev()).cut(k).rev();
  }
  inline poly operator/(const poly &b) const { return getdiv(b); }
  inline poly operator/=(const poly &b) { return *this = *this / b; }
  inline poly operator%(const poly &b) const {
    poly a = (*this);
    if (a.size() < b.size()) return a;
    poly r = (a - (a / b) * b);
    r.normalize();
    return r;
  }
  inline poly operator%=(const poly &b) { return *this = *this % b; }
  inline poly der() const {
    poly a = (*this);
    vector<int> ans;
    for (int i = 1; i < a.size(); i++) ans.push_back(1LL * i * a[i] % MOD);
    return poly(ans);
  }
  inline poly integral() const {
    poly a = (*this);
    vector<int> ans;
    ans.push_back(0);
    for (int i = 0; i < (int)a.size() - 1; i++)
      ans.push_back(1LL * inv(i + 1) * a[i] % MOD);
    return poly(ans);
  }
};
inline poly log(poly a) {
  poly b = a;
  b = b.der();
  poly x = a.invp();
  b *= x;
  b.resize(a.size());
  b = b.integral();
  b[0] = 0;
  return b;
}
inline poly exp(poly f) {
  poly a(1);
  for (int n = 1; n < (int)f.size(); n <<= 1) {
    while (a.size() < n + n) a.push_back(0);
    poly ca = f.cut(n + n);
    a += (ca - log(a)) * a;
    a = a.cut(n + n);
  }
  a.resize(f.size());
  return a;
}
const int D = 10;
int n, k;
poly power(poly x, int k) {
  if (k == 1) return x;
  poly t = power(x, k >> 1);
  t *= t;
  if (k & 1) t *= x;
  return t;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  poly p = poly(10);
  for (int i = 0; i < 10; i++) p[i] = 0;
  cin >> n >> k;
  for (int i = 0; i < k; i++) {
    int d;
    cin >> d;
    p[d]++;
  }
  poly u = power(p, (n / 2));
  long long ans = 0;
  for (int i = 0; i < u.size(); i++) ans += (1LL * u[i] * u[i]) % MOD;
  cout << (ans % MOD);
  return 0;
}