#include <bits/stdc++.h>
using namespace std;
const int N = 1e7, M = 2e1 + 7;
const long long mod = 998244353;
bool flag;
int n, k, lim, len, r[N], s[N], ans[N], rev[N];
inline int read() {
  int num = 0;
  char g = getchar();
  while (g < 48 || 57 < g) g = getchar();
  while (47 < g && g < 58)
    num = (num << 1) + (num << 3) + g - 48, g = getchar();
  return num;
}
inline int pows(long long a, int b) {
  long long ans = 1;
  while (b > 0) {
    if (b & 1) ans = (ans * a) % mod;
    a = (a * a) % mod, b = b >> 1;
  }
  return ans;
}
inline void NTT(int *s, int x) {
  for (int i = 0; i < lim; i++)
    if (r[i] < i) swap(s[i], s[r[i]]);
  for (int mid = 1; mid < lim; mid = mid << 1) {
    long long w = pows(x, (mod - 1) / (mid << 1));
    for (int i = 0, r = mid << 1; i < lim; i += r) {
      long long wn = 1;
      for (int j = 0; j < mid; j++, wn = (wn * w) % mod) {
        int a = s[i + j], b = (wn * s[i + j + mid]) % mod;
        s[i + j] = a + b, s[i + j + mid] = a - b + mod;
        if (s[i + j] >= mod) s[i + j] -= mod;
        if (s[i + j + mid] >= mod) s[i + j + mid] -= mod;
      }
    }
  }
}
int main() {
  n = read(), k = read(), len = 9, n = n >> 1;
  for (int i = 1; i <= k; i++) s[read()]++;
  while (n > 0) {
    lim = 1, k = 0;
    while (lim < len) lim = lim << 1, k++;
    lim = lim << 1, k++;
    long long invs = pows(lim, mod - 2);
    for (int i = 0; i < lim; i++)
      r[i] = (r[i >> 1] >> 1) | ((i & 1) << (k - 1));
    NTT(s, 3);
    if (n & 1) {
      if (!flag) {
        flag = true;
        for (int x = 0; x < lim; x++) ans[x] = s[x];
      } else {
        NTT(ans, 3);
        for (int x = 0; x < lim; x++)
          ans[x] = ((long long)(ans[x]) * s[x]) % mod;
      }
      NTT(ans, pows(3, mod - 2));
      for (int x = 0; x < lim; x++) ans[x] = invs * ans[x] % mod;
    }
    for (int i = 0; i < lim; i++) s[i] = (long long)(s[i]) * s[i] % mod;
    NTT(s, pows(3, mod - 2));
    for (int i = 0; i < lim; i++) s[i] = invs * s[i] % mod;
    len = (len << 1), n = n >> 1;
  }
  long long sum = 0;
  for (int i = 0; i <= 5e6; i++)
    sum = (sum + (long long)(ans[i]) * ans[i]) % mod;
  cout << sum << 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 N = 1e7, M = 2e1 + 7;
const long long mod = 998244353;
bool flag;
int n, k, lim, len, r[N], s[N], ans[N], rev[N];
inline int read() {
  int num = 0;
  char g = getchar();
  while (g < 48 || 57 < g) g = getchar();
  while (47 < g && g < 58)
    num = (num << 1) + (num << 3) + g - 48, g = getchar();
  return num;
}
inline int pows(long long a, int b) {
  long long ans = 1;
  while (b > 0) {
    if (b & 1) ans = (ans * a) % mod;
    a = (a * a) % mod, b = b >> 1;
  }
  return ans;
}
inline void NTT(int *s, int x) {
  for (int i = 0; i < lim; i++)
    if (r[i] < i) swap(s[i], s[r[i]]);
  for (int mid = 1; mid < lim; mid = mid << 1) {
    long long w = pows(x, (mod - 1) / (mid << 1));
    for (int i = 0, r = mid << 1; i < lim; i += r) {
      long long wn = 1;
      for (int j = 0; j < mid; j++, wn = (wn * w) % mod) {
        int a = s[i + j], b = (wn * s[i + j + mid]) % mod;
        s[i + j] = a + b, s[i + j + mid] = a - b + mod;
        if (s[i + j] >= mod) s[i + j] -= mod;
        if (s[i + j + mid] >= mod) s[i + j + mid] -= mod;
      }
    }
  }
}
int main() {
  n = read(), k = read(), len = 9, n = n >> 1;
  for (int i = 1; i <= k; i++) s[read()]++;
  while (n > 0) {
    lim = 1, k = 0;
    while (lim < len) lim = lim << 1, k++;
    lim = lim << 1, k++;
    long long invs = pows(lim, mod - 2);
    for (int i = 0; i < lim; i++)
      r[i] = (r[i >> 1] >> 1) | ((i & 1) << (k - 1));
    NTT(s, 3);
    if (n & 1) {
      if (!flag) {
        flag = true;
        for (int x = 0; x < lim; x++) ans[x] = s[x];
      } else {
        NTT(ans, 3);
        for (int x = 0; x < lim; x++)
          ans[x] = ((long long)(ans[x]) * s[x]) % mod;
      }
      NTT(ans, pows(3, mod - 2));
      for (int x = 0; x < lim; x++) ans[x] = invs * ans[x] % mod;
    }
    for (int i = 0; i < lim; i++) s[i] = (long long)(s[i]) * s[i] % mod;
    NTT(s, pows(3, mod - 2));
    for (int i = 0; i < lim; i++) s[i] = invs * s[i] % mod;
    len = (len << 1), n = n >> 1;
  }
  long long sum = 0;
  for (int i = 0; i <= 5e6; i++)
    sum = (sum + (long long)(ans[i]) * ans[i]) % mod;
  cout << sum << endl;
  return 0;
}

```