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;
namespace fft {
int len, last = -1, step = 0, rev[1 << 20];
long long C[1 << 20], D[1 << 20], P[1 << 20], Q[1 << 20];
struct complx {
  long double real, img;
  inline complx() { real = img = 0.0; }
  inline complx conjugate() { return complx(real, -img); }
  inline complx(long double x) { real = x, img = 0.0; }
  inline complx(long double x, long double y) { real = x, img = y; }
  inline complx operator+(complx other) {
    return complx(real + other.real, img + other.img);
  }
  inline complx operator-(complx other) {
    return complx(real - other.real, img - other.img);
  }
  inline complx operator*(complx other) {
    return complx((real * other.real) - (img * other.img),
                  (real * other.img) + (img * other.real));
  }
} u[1 << 20], v[1 << 20], f[1 << 20], g[1 << 20], dp[1 << 20], inv[1 << 20];
void build(int& a, long long* A, int& b, long long* B) {
  while (a > 1 && A[a - 1] == 0) a--;
  while (b > 1 && B[b - 1] == 0) b--;
  len = 1 << (32 - __builtin_clz(a + b) - (__builtin_popcount(a + b) == 1));
  for (int i = a; i < len; i++) A[i] = 0;
  for (int i = b; i < len; i++) B[i] = 0;
  if (!step++) {
    dp[1] = inv[1] = complx(1);
    for (int i = 1; (1 << i) < 1 << 20; i++) {
      double theta = (2.0 * acos(0.0)) / (1 << i);
      complx mul = complx(cos(theta), sin(theta));
      complx inv_mul = complx(cos(-theta), sin(-theta));
      int lim = 1 << i;
      for (int j = lim >> 1; j < lim; j++) {
        dp[2 * j] = dp[j], inv[2 * j] = inv[j];
        inv[2 * j + 1] = inv[j] * inv_mul;
        dp[2 * j + 1] = dp[j] * mul;
      }
    }
  }
  if (last != len) {
    last = len;
    int bit = (32 - __builtin_clz(len) - (__builtin_popcount(len) == 1));
    for (int i = 0; i < len; i++)
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (bit - 1));
  }
}
void transform(complx* in, complx* out, complx* ar) {
  for (int i = 0; i < len; i++) out[i] = in[rev[i]];
  for (int k = 1; k < len; k <<= 1) {
    for (int i = 0; i < len; i += (k << 1)) {
      for (int j = 0; j < k; j++) {
        complx z = out[i + j + k] * ar[j + k];
        out[i + j + k] = out[i + j] - z;
        out[i + j] = out[i + j] + z;
      }
    }
  }
}
void transform_unrolled(complx* in, complx* out, complx* ar) {
  for (int i = 0; i < len; i++) out[i] = in[rev[i]];
  for (int k = 1; k < len; k <<= 1) {
    for (int i = 0; i < len; i += (k << 1)) {
      complx z, *a = out + i, *b = out + i + k, *c = ar + k;
      if (k == 1) {
        z = (*b) * (*c);
        *b = *a - z, *a = *a + z;
      }
      for (int j = 0; j < k && k > 1; j += 2, a++, b++, c++) {
        z = (*b) * (*c);
        *b = *a - z, *a = *a + z;
        a++, b++, c++;
        z = (*b) * (*c);
        *b = *a - z, *a = *a + z;
      }
    }
  }
}
bool equals(int a, long long* A, int b, long long* B) {
  if (a != b) return false;
  for (a = 0; a < b && A[a] == B[a]; a++) {
  }
  return (a == b);
}
int square(int a, long long* A) {
  build(a, A, a, A);
  for (int i = 0; i < len; i++) u[i] = complx(A[i], 0);
  transform_unrolled(u, f, dp);
  for (int i = 0; i < len; i++) u[i] = f[i] * f[i];
  transform_unrolled(u, f, inv);
  for (int i = 0; i < len; i++) A[i] = (f[i].real / (long double)len) + 0.5;
  return a + a - 1;
}
int multiply(int a, long long* A, int b, long long* B) {
  if (equals(a, A, b, B)) return square(a, A);
  build(a, A, b, B);
  for (int i = 0; i < len; i++) u[i] = complx(A[i], B[i]);
  transform_unrolled(u, f, dp);
  for (int i = 0; i < len; i++) {
    int j = (len - 1) & (len - i);
    u[i] = (f[j] * f[j] - f[i].conjugate() * f[i].conjugate()) *
           complx(0, -0.25 / len);
  }
  transform_unrolled(u, f, dp);
  for (int i = 0; i < len; i++) A[i] = f[i].real + 0.5;
  return a + b - 1;
}
int mod_multiply(int a, long long* A, int b, long long* B, int mod) {
  build(a, A, b, B);
  int flag = equals(a, A, b, B);
  for (int i = 0; i < len; i++) A[i] %= mod, B[i] %= mod;
  for (int i = 0; i < len; i++) u[i] = complx(A[i] & 32767, A[i] >> 15);
  for (int i = 0; i < len; i++) v[i] = complx(B[i] & 32767, B[i] >> 15);
  transform_unrolled(u, f, dp);
  for (int i = 0; i < len; i++) g[i] = f[i];
  if (!flag) transform_unrolled(v, g, dp);
  for (int i = 0; i < len; i++) {
    int j = (len - 1) & (len - i);
    complx c1 = f[j].conjugate(), c2 = g[j].conjugate();
    complx a1 = (f[i] + c1) * complx(0.5, 0);
    complx a2 = (f[i] - c1) * complx(0, -0.5);
    complx b1 = (g[i] + c2) * complx(0.5 / len, 0);
    complx b2 = (g[i] - c2) * complx(0, -0.5 / len);
    v[j] = a1 * b2 + a2 * b1;
    u[j] = a1 * b1 + a2 * b2 * complx(0, 1);
  }
  transform_unrolled(u, f, dp);
  transform_unrolled(v, g, dp);
  long long x, y, z;
  for (int i = 0; i < len; i++) {
    x = f[i].real + 0.5, y = g[i].real + 0.5, z = f[i].img + 0.5;
    A[i] = (x + ((y % mod) << 15) + ((z % mod) << 30)) % mod;
  }
  return a + b - 1;
}
int long_multiply(int a, long long* A, int b, long long* B) {
  int mod1 = 1.5e9;
  int mod2 = mod1 + 1;
  for (int i = 0; i < a; i++) C[i] = A[i];
  for (int i = 0; i < b; i++) D[i] = B[i];
  mod_multiply(a, A, b, B, mod1);
  mod_multiply(a, C, b, D, mod2);
  for (int i = 0; i < len; i++) {
    A[i] =
        A[i] + (C[i] - A[i] + (long long)mod2) * (long long)mod1 % mod2 * mod1;
  }
  return a + b - 1;
}
int build_convolution(int n, long long* A, long long* B) {
  int i, m, d = 0;
  for (i = 0; i < n; i++) Q[i] = Q[i + n] = B[i];
  for (i = 0; i < n; i++) P[i] = A[i], P[i + n] = 0;
  n *= 2, m = 1 << (32 - __builtin_clz(n) - (__builtin_popcount(n) == 1));
  for (i = n; i < m; i++) P[i] = Q[i] = 0;
  return n;
}
void convolution(int n, long long* A, long long* B) {
  int len = build_convolution(n, A, B);
  multiply(len, P, len, Q);
  for (int i = 0; i < n; i++) A[i] = P[i + n];
}
void mod_convolution(int n, long long* A, long long* B, int mod) {
  int len = build_convolution(n, A, B);
  mod_multiply(len, P, len, Q, mod);
  for (int i = 0; i < n; i++) A[i] = P[i + n];
}
void long_convolution(int n, long long* A, long long* B) {
  int len = build_convolution(n, A, B);
  long_multiply(len, P, len, Q);
  for (int i = 0; i < n; i++) A[i] = P[i + n];
}
vector<int> hamming_distance(const char* str, const char* pattern) {
  int n = strlen(str), m = strlen(pattern);
  for (int i = 0; i < n; i++) P[i] = Q[i] = 0;
  for (int i = 0; i < n; i++) P[i] = str[i] == '1' ? 1 : -1;
  for (int i = 0, j = m - 1; j >= 0; i++, j--)
    Q[i] = pattern[j] == '1' ? 1 : -1;
  vector<int> res;
  fft::multiply(n, P, m, Q);
  for (int i = 0; (i + m) <= n; i++) {
    res.push_back(m - ((P[i + m - 1] + m) >> 1));
  }
  return res;
}
}  // namespace fft
int n, m;
long long A[1 << 20], B[1 << 20];
int bigmod(int p) {
  if (p == 1) return 10;
  int x = bigmod(p / 2);
  x = fft::mod_multiply(x, A, x, A, 998244353);
  if (p & 1) {
    x = fft::mod_multiply(x, A, 10, B, 998244353);
  }
  return x;
}
int main() {
  scanf("%d", &n);
  scanf("%d", &m);
  int x;
  for (int i = 0; i < m; i++) {
    scanf("%d", &x);
    A[x] = 1;
    B[x] = 1;
  }
  x = bigmod(n / 2);
  long long ans = 0;
  for (int i = 0; i < x; i++) {
    if (A[i]) {
      ans += (A[i] * A[i]);
      ans %= 998244353;
    }
  }
  cout << ans << endl;
}