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;
const int P = 998244353, R = 3;
void exGcd(int a, int b, int& x, int& y) {
  if (!b) {
    x = 1;
    y = 0;
    return;
  }
  exGcd(b, a % b, y, x);
  y -= a / b * x;
}
int inv(int a) {
  int x, y;
  exGcd(a, P, x, y);
  if (x < 0) x += P;
  return x;
}
int mpow(int x, int k) {
  int ret = 1;
  while (k) {
    if (k & 1) ret = ret * (long long)x % P;
    x = x * (long long)x % P;
    k >>= 1;
  }
  return ret;
}
struct Simple {
  int n;
  vector<int> fac, ifac, inv;
  void build(int n) {
    this->n = n;
    fac.resize(n + 1);
    ifac.resize(n + 1);
    inv.resize(n + 1);
    fac[0] = 1;
    for (int x = 1; x <= n; ++x) fac[x] = fac[x - 1] * (long long)x % P;
    inv[1] = 1;
    for (int x = 2; x <= n; ++x)
      inv[x] = -(P / x) * (long long)inv[P % x] % P + P;
    ifac[0] = 1;
    for (int x = 1; x <= n; ++x) ifac[x] = ifac[x - 1] * (long long)inv[x] % P;
  }
  Simple() { build(1); }
  void check(int k) {
    int nn = n;
    if (k > nn) {
      while (k > nn) nn <<= 1;
      build(nn);
    }
  }
  int gfac(int k) {
    check(k);
    return fac[k];
  }
  int gifac(int k) {
    check(k);
    return ifac[k];
  }
  int ginv(int k) {
    check(k);
    return inv[k];
  }
  int binom(int n, int m) {
    if (m < 0 || m > n) return 0;
    return gfac(n) * (long long)gifac(m) % P * gifac(n - m) % P;
  }
} simp;
const int L2 = 11;
struct NumberTheoreticTransform {
  int brev[1 << L2];
  NumberTheoreticTransform() {
    for (int i = 1; i < (1 << L2); ++i)
      brev[i] = brev[i >> 1] >> 1 | ((i & 1) << (L2 - 1));
  }
  void fft(int* a, int lgn, int d) {
    int n = 1 << lgn;
    for (int i = 0; i < n; ++i) {
      int rev = (brev[i >> L2] | (brev[i & ((1 << L2) - 1)] << L2)) >>
                ((L2 << 1) - lgn);
      if (i < rev) swap(a[i], a[rev]);
    }
    int rt = d == 1 ? R : inv(R);
    for (int i = 0; i < lgn; ++i) {
      int t = 1 << i;
      int omega = mpow(rt, (P - 1) >> (i + 1));
      for (int j = 0; j < n; j += t << 1) {
        int w = 1;
        for (int k = 0; k < t; ++k) {
          int a0 = a[j + k], a1 = a[j + k + t];
          a[j + k] = (a0 + w * (long long)a1) % P;
          a[j + k + t] = (a0 + (P - w) * (long long)a1) % P;
          w = w * (long long)omega % P;
        }
      }
    }
    if (d == -1) {
      int in = inv(n);
      for (int i = 0; i < n; ++i) a[i] = a[i] * (long long)in % P;
    }
  }
} ntt;
struct Poly {
  vector<int> a;
  Poly(int v = 0) : a(1) {
    if ((v %= P) < 0) v += P;
    a[0] = v;
  }
  Poly(const vector<int>& a) : a(a) {}
  Poly(initializer_list<int> init) : a(init) {}
  int operator[](int k) const { return k < a.size() ? a[k] : 0; }
  int& operator[](int k) {
    if (k >= a.size()) a.resize(k + 1);
    return a[k];
  }
  int deg() const { return a.size() - 1; }
  void redeg(int d) { a.resize(d + 1); }
  Poly slice(int d) const {
    if (d < a.size()) return vector<int>(a.begin(), a.begin() + d + 1);
    vector<int> res(a);
    res.resize(d + 1);
    return res;
  }
  int* base() { return a.begin().base(); }
  const int* base() const { return a.begin().base(); }
  void println(FILE* fp) const {
    fprintf(fp, "%d", a[0]);
    for (int i = 1; i < a.size(); ++i) fprintf(fp, " %d", a[i]);
    fputc('\n', fp);
  }
  Poly operator+(const Poly& rhs) const {
    vector<int> res(max(a.size(), rhs.a.size()));
    for (int i = 0; i < res.size(); ++i)
      if ((res[i] = operator[](i) + rhs[i]) >= P) res[i] -= P;
    return res;
  }
  Poly operator-() const {
    Poly ret(a);
    for (int i = 0; i < a.size(); ++i)
      if (ret[i]) ret[i] = P - ret[i];
    return ret;
  }
  Poly operator-(const Poly& rhs) const { return operator+(-rhs); }
  Poly operator*(const Poly& rhs) const;
  Poly operator/(const Poly& rhs) const;
  Poly operator%(const Poly& rhs) const;
  Poly sq() const;
  Poly inv() const;
  Poly sqrt() const;
  Poly ln() const;
  Poly exp() const;
  Poly shift(int k) const;
};
Poly operator"" _z(unsigned long long a) { return {0, (int)a}; }
Poly operator+(int v, const Poly& rhs) { return Poly(v) + rhs; }
Poly zeroes(int deg) { return vector<int>(deg + 1); }
Poly Poly::operator*(const Poly& rhs) const {
  int n = deg(), m = rhs.deg();
  if (n <= 10 || m <= 10) {
    Poly ret = zeroes(n + m);
    for (int i = 0; i <= n; ++i)
      for (int j = 0; j <= m; ++j)
        ret[i + j] = (ret[i + j] + a[i] * (long long)rhs[j]) % P;
    return ret;
  }
  n += m;
  int l = 0;
  while ((1 << l) <= n) ++l;
  vector<int> res(1 << l), tmp(1 << l);
  memcpy(res.begin().base(), base(), a.size() * sizeof(int));
  ntt.fft(res.begin().base(), l, 1);
  memcpy(tmp.begin().base(), rhs.base(), rhs.a.size() * sizeof(int));
  ntt.fft(tmp.begin().base(), l, 1);
  for (int i = 0; i < (1 << l); ++i) res[i] = res[i] * (long long)tmp[i] % P;
  ntt.fft(res.begin().base(), l, -1);
  res.resize(n + 1);
  return res;
}
Poly Poly::inv() const {
  Poly g = ::inv(a[0]);
  int t = 0;
  for (int n = 1; n <= deg(); ++t, n <<= 1) {
    Poly nttg = g;
    nttg.redeg((n << 1) - 1);
    ntt.fft(nttg.base(), t + 1, 1);
    Poly prod = slice((n << 1) - 1);
    ntt.fft(prod.base(), t + 1, 1);
    for (int i = 0; i < (n << 1); ++i)
      prod[i] = prod[i] * (long long)nttg[i] % P;
    ntt.fft(prod.base(), t + 1, -1);
    for (int i = 0; i < n; ++i) prod[i] = 0;
    ntt.fft(prod.base(), t + 1, 1);
    for (int i = 0; i < (n << 1); ++i)
      prod[i] = prod[i] * (long long)nttg[i] % P;
    ntt.fft(prod.base(), t + 1, -1);
    for (int i = 0; i < n; ++i) prod[i] = 0;
    g = g - prod;
  }
  g.redeg(deg());
  return g;
}
Poly Poly::shift(int k) const {
  int n = deg();
  Poly t = zeroes(n);
  simp.check(n);
  for (int i = 0; i <= n; ++i) t[n - i] = a[i] * (long long)simp.fac[i] % P;
  int pw = 1;
  Poly help = vector<int>(simp.ifac.begin(), simp.ifac.begin() + n + 1);
  for (int i = 0; i <= n; ++i) {
    help[i] = help[i] * (long long)pw % P;
    pw = pw * (long long)k % P;
  }
  t = t * help;
  for (int i = 0; i <= n; ++i) help[i] = t[n - i] * (long long)simp.ifac[i] % P;
  return help;
}
const int N = 200100;
int n, k;
int main() {
  scanf("%d%d", &n, &k);
  Poly a = zeroes(9 * (n >> 1) + 1);
  while (k--) {
    int d;
    scanf("%d", &d);
    ++a[d];
  }
  int l = 0;
  while ((1 << l) < a.a.size()) ++l;
  a.a.resize(1 << l);
  ntt.fft(a.base(), l, 1);
  for (int i = 0; i < (1 << l); ++i) a[i] = mpow(a[i], n >> 1);
  ntt.fft(a.base(), l, -1);
  int ans = 0;
  for (int v : a.a) {
    ans = (ans + v * (long long)v) % P;
  }
  printf("%d\n", ans);
  return 0;
}