#include <bits/stdc++.h>
using namespace std;
const long long MODULE = 998244353;
const int MAXPOLY = 1048576;
long long add(long long a, long long b) {
  long long res = a + b;
  res %= MODULE;
  return res;
}
long long mul(long long a, long long b) {
  long long res = a * b;
  res %= MODULE;
  return res;
}
long long bin_mod_pow(long long val, long long pow) {
  long long res = 1;
  long long tmp = val;
  while (pow) {
    if (pow & 1) {
      res = mul(res, tmp);
    }
    pow >>= 1;
    tmp = mul(tmp, tmp);
  }
  return res;
}
long long invert(long long num) { return bin_mod_pow(num, MODULE - 2); }
namespace FFT {
const int mod = MODULE;
long long root = bin_mod_pow(3, 8 * 7 * 17);
long long root_1 = invert(root);
const long long root_pw = 1 << 20;
int buf[root_pw];
void Calc(bool inv) {
  int n = root_pw;
  for (int i = 1, j = 0; i < n; ++i) {
    int bit = n >> 1;
    for (; j >= bit; bit >>= 1) j -= bit;
    j += bit;
    if (i < j) swap(buf[i], buf[j]);
  }
  for (int len = 2; len <= n; len <<= 1) {
    int wlen = inv ? root_1 : root;
    for (int i = len; i < root_pw; i <<= 1) wlen = int(wlen * 1ll * wlen % mod);
    for (int i = 0; i < n; i += len) {
      int w = 1;
      for (int j = 0; j < len / 2; ++j) {
        int u = buf[i + j], v = int(buf[i + j + len / 2] * 1ll * w % mod);
        buf[i + j] = u + v < mod ? u + v : u + v - mod;
        buf[i + j + len / 2] = u - v >= 0 ? u - v : u - v + mod;
        w = int(w * 1ll * wlen % mod);
      }
    }
  }
  if (inv) {
    int nrev = invert(n);
    for (int i = 0; i < n; ++i) buf[i] = int(buf[i] * 1ll * nrev % mod);
  }
}
}  // namespace FFT
void solve() {
  int n, k;
  cin >> n >> k;
  vector<int> coeffs(MAXPOLY);
  for (int i = 0; i < 16; i++) {
    coeffs[i] = 0;
  }
  for (int i = 0; i < k; i++) {
    int dk;
    cin >> dk;
    coeffs[dk] = 1;
  }
  for (int i = 0; i < MAXPOLY; i++) {
    FFT::buf[i] = coeffs[i];
  }
  FFT::Calc(false);
  for (int i = 0; i < MAXPOLY; i++) {
    FFT::buf[i] = bin_mod_pow(FFT::buf[i], n / 2);
  }
  FFT::Calc(true);
  long long res = 0;
  for (int i = 0; i < MAXPOLY; i++) {
    long long tmp = FFT::buf[i];
    tmp = mul(tmp, tmp);
    res = add(res, tmp);
  }
  cout << res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  solve();
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long MODULE = 998244353;
const int MAXPOLY = 1048576;
long long add(long long a, long long b) {
  long long res = a + b;
  res %= MODULE;
  return res;
}
long long mul(long long a, long long b) {
  long long res = a * b;
  res %= MODULE;
  return res;
}
long long bin_mod_pow(long long val, long long pow) {
  long long res = 1;
  long long tmp = val;
  while (pow) {
    if (pow & 1) {
      res = mul(res, tmp);
    }
    pow >>= 1;
    tmp = mul(tmp, tmp);
  }
  return res;
}
long long invert(long long num) { return bin_mod_pow(num, MODULE - 2); }
namespace FFT {
const int mod = MODULE;
long long root = bin_mod_pow(3, 8 * 7 * 17);
long long root_1 = invert(root);
const long long root_pw = 1 << 20;
int buf[root_pw];
void Calc(bool inv) {
  int n = root_pw;
  for (int i = 1, j = 0; i < n; ++i) {
    int bit = n >> 1;
    for (; j >= bit; bit >>= 1) j -= bit;
    j += bit;
    if (i < j) swap(buf[i], buf[j]);
  }
  for (int len = 2; len <= n; len <<= 1) {
    int wlen = inv ? root_1 : root;
    for (int i = len; i < root_pw; i <<= 1) wlen = int(wlen * 1ll * wlen % mod);
    for (int i = 0; i < n; i += len) {
      int w = 1;
      for (int j = 0; j < len / 2; ++j) {
        int u = buf[i + j], v = int(buf[i + j + len / 2] * 1ll * w % mod);
        buf[i + j] = u + v < mod ? u + v : u + v - mod;
        buf[i + j + len / 2] = u - v >= 0 ? u - v : u - v + mod;
        w = int(w * 1ll * wlen % mod);
      }
    }
  }
  if (inv) {
    int nrev = invert(n);
    for (int i = 0; i < n; ++i) buf[i] = int(buf[i] * 1ll * nrev % mod);
  }
}
}  // namespace FFT
void solve() {
  int n, k;
  cin >> n >> k;
  vector<int> coeffs(MAXPOLY);
  for (int i = 0; i < 16; i++) {
    coeffs[i] = 0;
  }
  for (int i = 0; i < k; i++) {
    int dk;
    cin >> dk;
    coeffs[dk] = 1;
  }
  for (int i = 0; i < MAXPOLY; i++) {
    FFT::buf[i] = coeffs[i];
  }
  FFT::Calc(false);
  for (int i = 0; i < MAXPOLY; i++) {
    FFT::buf[i] = bin_mod_pow(FFT::buf[i], n / 2);
  }
  FFT::Calc(true);
  long long res = 0;
  for (int i = 0; i < MAXPOLY; i++) {
    long long tmp = FFT::buf[i];
    tmp = mul(tmp, tmp);
    res = add(res, tmp);
  }
  cout << res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  solve();
  return 0;
}

```