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(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#pragma GCC optimize( \
    "inline,-fgcse,-fgcse-lm,-fipa-sra,-ftree-pre,-ftree-vrp,-fpeephole2,-ffast-math,-fsched-spec,unroll-loops,-falign-jumps,-falign-loops,-falign-labels,-fdevirtualize,-fcaller-saves,-fcrossjumping,-fthread-jumps,-funroll-loops,-freorder-blocks,-fschedule-insns,inline-functions,-ftree-tail-merge,-fschedule-insns2,-fstrict-aliasing,-fstrict-overflow,-falign-functions,-fcse-follow-jumps,-fsched-interblock,-fpartial-inlining,no-stack-protector,-freorder-functions,-findirect-inlining,-fhoist-adjacent-loads,-frerun-cse-after-loop,inline-small-functions,-finline-small-functions,-ftree-switch-conversion,-foptimize-sibling-calls,-fexpensive-optimizations,inline-functions-called-once,-fdelete-null-pointer-checks")
using namespace std;
using db = double;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int, int>;
template <class T>
void cmax(T& x, const T& y) {
  if (x < y) x = y;
}
template <class T>
void cmin(T& x, const T& y) {
  if (x > y) x = y;
}
template <class T>
void sort(vector<T>& v) {
  sort(v.begin(), v.end());
}
template <class T>
void reverse(vector<T>& v) {
  reverse(v.begin(), v.end());
}
template <class T>
void unique(vector<T>& v) {
  sort(v.begin(), v.end()), v.erase(unique(v.begin(), v.end()), v.end());
}
void reverse(string& s) { reverse(s.begin(), s.end()); }
const int io_size = 1 << 23 | 233;
const int io_limit = 1 << 22;
struct io_in {
  char ch;
  char getchar() {
    static char buf[io_size], *p1 = buf, *p2 = buf;
    return (p1 == p2) &&
                   (p2 = (p1 = buf) + fread(buf, 1, io_size, stdin), p1 == p2)
               ? EOF
               : *p1++;
  }
  io_in& operator>>(char& c) {
    for (c = getchar(); isspace(c); c = getchar())
      ;
    return *this;
  }
  io_in& operator>>(string& s) {
    for (s.clear(); isspace(ch = getchar());)
      ;
    if (!~ch) return *this;
    for (s = ch; !isspace(ch = getchar()) && ~ch; s += ch)
      ;
    return *this;
  }
  io_in& operator>>(char* str) {
    char* cur = str;
    while (*cur) *cur++ = 0;
    for (cur = str; isspace(ch = getchar());)
      ;
    if (!~ch) return *this;
    for (*cur = ch; !isspace(ch = getchar()) && ~ch; *++cur = ch)
      ;
    return *++cur = 0, *this;
  }
  template <class T>
  void read(T& x) {
    bool f = 0;
    while ((ch = getchar()) < 48 && ~ch) f ^= (ch == 45);
    x = ~ch ? (ch ^ 48) : 0;
    while ((ch = getchar()) > 47) x = x * 10 + (ch ^ 48);
    x = f ? -x : x;
  }
  io_in& operator>>(int& x) { return read(x), *this; }
  io_in& operator>>(ll& x) { return read(x), *this; }
  io_in& operator>>(uint& x) { return read(x), *this; }
  io_in& operator>>(ull& x) { return read(x), *this; }
  io_in& operator>>(db& x) {
    read(x);
    bool f = x < 0;
    x = f ? -x : x;
    if (ch ^ '.') return *this;
    double d = 0.1;
    while ((ch = getchar()) > 47) x += d * (ch ^ 48), d *= .1;
    return x = f ? -x : x, *this;
  }
} in;
struct io_out {
  char buf[io_size], *s = buf;
  int pw[233], st[233];
  io_out() {
    set(7);
    for (register int i = (pw[0] = 1); i <= (9); ++i) pw[i] = pw[i - 1] * 10;
  }
  ~io_out() { flush(); }
  void io_chk() {
    if (s - buf > io_limit) flush();
  }
  void flush() { fwrite(buf, 1, s - buf, stdout), fflush(stdout), s = buf; }
  io_out& operator<<(char c) { return *s++ = c, *this; }
  io_out& operator<<(string str) {
    for (char c : str) *s++ = c;
    return io_chk(), *this;
  }
  io_out& operator<<(char* str) {
    char* cur = str;
    while (*cur) *s++ = *cur++;
    return io_chk(), *this;
  }
  template <class T>
  void write(T x) {
    if (x < 0) *s++ = '-', x = -x;
    do {
      st[++st[0]] = x % 10, x /= 10;
    } while (x);
    while (st[0]) *s++ = st[st[0]--] ^ 48;
  }
  io_out& operator<<(int x) { return write(x), io_chk(), *this; }
  io_out& operator<<(ll x) { return write(x), io_chk(), *this; }
  io_out& operator<<(uint x) { return write(x), io_chk(), *this; }
  io_out& operator<<(ull x) { return write(x), io_chk(), *this; }
  int len, lft, rig;
  void set(int _length) { len = _length; }
  io_out& operator<<(db x) {
    bool f = x < 0;
    x = f ? -x : x, lft = x, rig = 1. * (x - lft) * pw[len];
    return write(f ? -lft : lft), *s++ = '.', write(rig), io_chk(), *this;
  }
} out;
template <long long sz, long long mod>
struct math_t {
  math_t() {
    fac.resize(sz + 1), ifac.resize(sz + 1);
    for (register long long i = (fac[0] = 1); i <= (sz); ++i)
      fac[i] = fac[i - 1] * i % mod;
    ifac[sz] = inv(fac[sz]);
    for (register long long i = (sz - 1); i >= (0); --i)
      ifac[i] = ifac[i + 1] * (i + 1) % mod;
  }
  vector<long long> fac, ifac;
  long long qpow(long long x, long long y) {
    long long ans = 1;
    for (; y; y >>= 1, x = x * x % mod)
      if (y & 1) ans = ans * x % mod;
    return ans;
  }
  long long inv(long long x) { return qpow(x, mod - 2); }
  long long C(long long n, long long m) {
    if (n < 0 || m < 0 || n < m) return 0;
    return fac[n] * ifac[m] % mod * ifac[n - m] % mod;
  }
};
long long gcd(long long x, long long y) { return !y ? x : gcd(y, x % y); }
long long lcm(long long x, long long y) { return x * y / gcd(x, y); }
const long long maxn = 8e6 + 63;
const long long P = 998244353;
const long long G = 3;
const long long Gi = 332748118;
long long n, m, rev[maxn];
long long a[maxn], b[maxn];
long long limit = 1;
long long Inv = 0;
inline long long qpow(long long x, long long y) {
  long long ans = 1;
  for (; y; y >>= 1, x = x * x % P)
    if (y & 1) ans = ans * x % P;
  return ans;
}
inline long long inc(const long long& x, const long long& y) {
  return (x + y >= P) ? (x + y - P) : x + y;
}
inline long long dec(const long long& x, const long long& y) {
  return (x - y >= 0) ? x - y : (x - y + P);
}
inline void swap(long long& x, long long& y) { x ^= y ^= x ^= y; }
void NTT(long long* A, long long type) {
  for (register long long i = (0); i <= (limit); ++i)
    if (i < rev[i]) swap(A[i], A[rev[i]]);
  for (long long len = 1; len < limit; len <<= 1) {
    long long Wn = qpow(type == 1 ? G : Gi, (P ^ 1) / (len << 1));
    for (long long i = 0; i < limit; i += len << 1) {
      long long w = 1;
      for (long long j = 0, x, y; j < len; j++, w = w * Wn % P) {
        x = A[i + j], y = A[i + j + len] * w % P;
        A[i + j] = inc(x, y), A[i + j + len] = dec(x, y);
      }
    }
  }
  if (type == -1) {
    for (long long i = 0; i < limit; i++) A[i] = A[i] * Inv % P;
  }
}
void init(long long n) {
  limit = 1;
  long long l = 0;
  while (limit <= n) {
    limit <<= 1, ++l;
  }
  for (long long i = 0; i < limit; i++)
    rev[i] = rev[i >> 1] >> 1 | (i & 1) << l - 1;
  Inv = qpow(limit, P - 2);
}
signed main() {
  in >> n >> m;
  n >>= 1;
  while (m--) {
    long long x;
    in >> x;
    b[x] = 1;
  }
  a[0] = 1;
  init(10 << 2);
  while (n) {
    if (n & 1) {
      long long mx = 0;
      for (long long i = 0; i < limit; i++)
        if (b[i]) mx = i;
      init(mx << 2);
      NTT(a, 1), NTT(b, 1);
      for (long long i = 0; i < limit; i++) a[i] = a[i] * b[i] % P;
      NTT(a, -1), NTT(b, -1);
    }
    long long mx = 0;
    for (long long i = 0; i < limit; i++)
      if (b[i]) mx = i;
    init(mx << 2);
    NTT(b, 1);
    for (long long i = 0; i < limit; i++) b[i] = b[i] * b[i] % P;
    NTT(b, -1);
    n >>= 1;
  }
  long long ans = 0;
  for (long long i = 0; i < limit; i++) ans = inc(ans, (a[i] * a[i]) % P);
  out << ans << '\n';
  return 0;
}