#include <bits/stdc++.h>
using namespace std;
using namespace chrono;

using ll = long long;
using ull = unsigned long long;

string to_string(const string &s) {
  return '"' + s + '"';
}

string to_string(bool b) {
  return b ? "true" : "false";
}

template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename T>
string to_string(const T &v) {
  string s = "{";
  bool first = true;
  for (const auto &it : v) {
    if (!first)
      s += ", ";
    else
      first = false;
    s += to_string(it);
  }
  return s += "}";
}

void debug_out() {
  cerr << endl;
}

template <typename T, typename... Args>
void debug_out(const T &first, const Args&... rest) {
  cerr << to_string(first) << " ";
  debug_out(rest...);
}

#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

auto startTime = high_resolution_clock::now();
int get_time() {
  auto stopTime = chrono::high_resolution_clock::now();
  auto duration = duration_cast<milliseconds>(stopTime - startTime);
  return duration.count(); // in ms
}


const int MOD = 998244353;

constexpr int lgpow(int x, int p) {

  int aux = x, ans = 1;
  for (int i = 1; i <= p; i <<= 1) {
    if (i & p)
      ans = 1ll * ans * aux % MOD;
    aux = 1ll * aux * aux % MOD;
  }

  return ans;
}

constexpr int invmod(int x) {
  return lgpow(x, MOD - 2);
}

namespace NTT {
  vector<int> ntt( vector<int> &a, int g ) {
    int n = a.size();
    int lg = log2(n); 
    for ( int i = 0; i < n; ++i ) {
      int j = 0;
      for ( int b = 0; b < lg; ++b ) {
        j += ( ( ( i >> b ) & 1 ) << ( lg - b - 1 ) );
      }
      if ( j < i ) {
        swap(a[i], a[j]);
      }
    }

    for ( int l = 2; l <= n; l <<= 1 ) {
      int p = lgpow(g, n / l);
      for ( int b = 0; b < n; b += l ) {
        for ( int i = 0, t = 1; i < l / 2; ++i, t = (1ll * t * p) % MOD ) {
          int x = a[b + i], y = 1ll * a[b + i + l / 2] * t % MOD;
          a[b + i] = (x + y) % MOD;
          a[b + i + l / 2] = (1ll * MOD + x - y) % MOD;
        }
      }
    }
    return a;
  }

  vector<int> mul( vector<int> a, vector<int> b ) {
    int n = a.size() + b.size() - 1;
    int p2 = 1;
    while ( p2 < n ) {
      p2 *= 2;
    }
    n = p2;

    while ( a.size() < n ) {
      a.push_back(0);
    }

    while ( b.size() < n ) {
      b.push_back(0);
    } 

    auto ra = ntt(a, lgpow(3, MOD / n));
    auto rb = ntt(b, lgpow(3, MOD / n));

    for( int i = 0; i < ra.size(); ++i ) {
      ra[i] = 1ll * ra[i] * rb[i] % MOD;
    }

    ra = ntt(ra, lgpow(lgpow(3, MOD - 2), MOD / n));
    int inv = lgpow(ra.size(), MOD - 2);
    for( int i = 0; i < ra.size(); ++i ) {
      ra[i] = 1ll * ra[i] * inv % MOD;
    }
    while ( !ra.back() )
      ra.pop_back();  
    return ra;
  }
};

namespace comb {
  vector<int> fact, ifact;

  void init(int n) {
    fact.resize(n + 1);
    ifact.resize(n + 1);

    fact[0] = 1;
    for (int i = 1; i <= n; ++i) {
      fact[i] = 1LL * fact[i - 1] * i % MOD;
    }

    ifact[n] = invmod(fact[n]);
    for (int i = n - 1; i >= 0; --i) {
      ifact[i] = 1LL * ifact[i + 1] * (i + 1) % MOD;
    }
  }

  int comb(int n, int k) {
    return 1LL * fact[n] * ifact[k] % MOD * ifact[n - k] % MOD;
  }
}

vector<int> divide(int st, int dr, vector<int> &a) {
  if (st == dr) {
    return {a[st], 1};
  }

  int mij = (st + dr) / 2;

  auto l = divide(st, mij, a);
  auto r = divide(mij + 1, dr, a);

  return NTT::mul(l, r);
}

void solve() {
  int n;
  ll m;
  cin >> n >> m;

  vector<int> a(n + 1);
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
  }

  if (m == 1) {
    int p = 1;
    for (int i = 1; i <= n; ++i) {
      p = 1LL * p * (a[i] + 1) % MOD;
    }
    cout << p << "\n";
    return;
  }

  auto b = divide(1, n, a);

  vector<pair<int, int>> p;

  for (int i = 2; 1LL * i * i <= m; ++i) {
    int k = 0;
    while (m % i == 0) {
      m /= i;
      ++k;
    }

    if (k > 0)
      p.push_back({i % MOD, k});
  }

  if (m > 1)
    p.push_back({m % MOD, 1});

  vector<int> ans = b;
  comb::init(n + 50);
  for (auto [x, y] : p) {
    ans[0] = (ans[0] * comb::comb(y + n - 1, n - 1)) % MOD;
    for (int k = 1; k < n; ++k) {
      int c = 1;
      int sum = 0;
      for (int j = 0; j <= y; ++j) {
        sum = (sum + 1LL * c % MOD * comb::comb(k + j - 1, k - 1) % MOD 
                             * comb::comb(y - j + n - k - 1, n - k - 1)) % MOD;
        c = 1LL * c * x % MOD;
      }
      ans[k] = 1LL * ans[k] * sum % MOD;
    }

    ans[n] = (ans[n] * 1LL * lgpow(x, y) % MOD * comb::comb(y + n - 1, n - 1) % MOD) % MOD;
  }

  int sum = 0;
  for (auto it : ans)
    sum = (sum + it) % MOD;

  cout << sum << "\n";
}

int main() {
  cin.tie(NULL);
  ios_base::sync_with_stdio(false);

  int t = 1;
//  cin >> t;
  while (t--)
    solve();

  return 0;
}