#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
const int root_pw = 1 << 23;
const int root = 31;
const int root_1 = 128805723;
long long int ip(long long int a, long long int p) {
  if (!p) return 1;
  if (p & 1) return (a * ip(a, p - 1)) % mod;
  long long int ret = ip(a, p / 2);
  return (ret * ret) % mod;
}
int get_root() {
  int r, q;
  for (r = 2; r < mod; r++) {
    if (ip(r, root_pw) == 1) {
      for (q = 1; q < root_pw; q++)
        if (ip(r, q) == 1) break;
      if (q == root_pw) return r;
    }
  }
  return -1;
}
void fft(vector<int>& a, bool invert) {
  int n = (int)a.size();
  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(a[i], a[j]);
  }
  for (int len = 2; len <= n; len <<= 1) {
    int wlen = invert ? 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 = a[i + j], v = int(a[i + j + len / 2] * 1ll * w % mod);
        a[i + j] = u + v < mod ? u + v : u + v - mod;
        a[i + j + len / 2] = u - v >= 0 ? u - v : u - v + mod;
        w = int(w * 1ll * wlen % mod);
      }
    }
  }
  if (invert) {
    int nrev = ip(n, mod - 2);
    for (int i = 0; i < n; ++i) a[i] = int(a[i] * 1ll * nrev % mod);
  }
}
void multiply(const vector<int>& a, const vector<int>& b, vector<int>& res) {
  vector<int> fa(a.begin(), a.end()), fb(b.begin(), b.end());
  size_t n = 1;
  while (n < max(a.size(), b.size())) n <<= 1;
  n <<= 1;
  fa.resize(n), fb.resize(n);
  fft(fa, false), fft(fb, false);
  for (size_t i = 0; i < n; ++i) fa[i] = ((long long int)fa[i] * fb[i]) % mod;
  fft(fa, true);
  res.resize(n);
  for (size_t i = 0; i < n; ++i) res[i] = fa[i];
}
int valid[15];
vector<int> basic() {
  vector<int> ret;
  ret.resize(10);
  for (int i = 0; i < 10; i++)
    if (valid[i]) ret[i] = 1;
  return ret;
}
vector<int> ip(vector<int> a, int p) {
  vector<int> ret = {1};
  vector<int> aux = a;
  while (p) {
    if (p & 1) multiply(ret, aux, ret);
    multiply(aux, aux, aux);
    p = p / 2;
  }
  return ret;
}
vector<int> fin;
int main() {
  int n, k, d;
  scanf("%d %d", &n, &k);
  while (k--) {
    scanf("%d", &d);
    valid[d] = true;
  }
  fin = ip(basic(), n / 2);
  int ret = 0;
  for (auto x : fin) ret = (ret + (long long int)x * x) % mod;
  cout << ret << endl;
  return 0;
}

### Prompt

Please create a solution in Cpp to the following 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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
const int root_pw = 1 << 23;
const int root = 31;
const int root_1 = 128805723;
long long int ip(long long int a, long long int p) {
  if (!p) return 1;
  if (p & 1) return (a * ip(a, p - 1)) % mod;
  long long int ret = ip(a, p / 2);
  return (ret * ret) % mod;
}
int get_root() {
  int r, q;
  for (r = 2; r < mod; r++) {
    if (ip(r, root_pw) == 1) {
      for (q = 1; q < root_pw; q++)
        if (ip(r, q) == 1) break;
      if (q == root_pw) return r;
    }
  }
  return -1;
}
void fft(vector<int>& a, bool invert) {
  int n = (int)a.size();
  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(a[i], a[j]);
  }
  for (int len = 2; len <= n; len <<= 1) {
    int wlen = invert ? 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 = a[i + j], v = int(a[i + j + len / 2] * 1ll * w % mod);
        a[i + j] = u + v < mod ? u + v : u + v - mod;
        a[i + j + len / 2] = u - v >= 0 ? u - v : u - v + mod;
        w = int(w * 1ll * wlen % mod);
      }
    }
  }
  if (invert) {
    int nrev = ip(n, mod - 2);
    for (int i = 0; i < n; ++i) a[i] = int(a[i] * 1ll * nrev % mod);
  }
}
void multiply(const vector<int>& a, const vector<int>& b, vector<int>& res) {
  vector<int> fa(a.begin(), a.end()), fb(b.begin(), b.end());
  size_t n = 1;
  while (n < max(a.size(), b.size())) n <<= 1;
  n <<= 1;
  fa.resize(n), fb.resize(n);
  fft(fa, false), fft(fb, false);
  for (size_t i = 0; i < n; ++i) fa[i] = ((long long int)fa[i] * fb[i]) % mod;
  fft(fa, true);
  res.resize(n);
  for (size_t i = 0; i < n; ++i) res[i] = fa[i];
}
int valid[15];
vector<int> basic() {
  vector<int> ret;
  ret.resize(10);
  for (int i = 0; i < 10; i++)
    if (valid[i]) ret[i] = 1;
  return ret;
}
vector<int> ip(vector<int> a, int p) {
  vector<int> ret = {1};
  vector<int> aux = a;
  while (p) {
    if (p & 1) multiply(ret, aux, ret);
    multiply(aux, aux, aux);
    p = p / 2;
  }
  return ret;
}
vector<int> fin;
int main() {
  int n, k, d;
  scanf("%d %d", &n, &k);
  while (k--) {
    scanf("%d", &d);
    valid[d] = true;
  }
  fin = ip(basic(), n / 2);
  int ret = 0;
  for (auto x : fin) ret = (ret + (long long int)x * x) % mod;
  cout << ret << endl;
  return 0;
}

```