#pragma GCC optimize("O2")
#include <bits/extc++.h>
#include <algorithm>
#include <array>
#include <bit>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <compare>
#include <complex>
#include <concepts>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numbers>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <span>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>

#define int ll
#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

namespace R = std::ranges;
namespace V = std::views;

using namespace std;

using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
using tiii = tuple<int, int, int>;
using ldb = long double;
//#define double ldb

template<class T>
ostream& operator<<(ostream& os, const pair<T, T> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(const T &X : arr)
    os << X << ' ';
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(const T &X : vec)
    os << X << ' ';
  return os;
}

/**
 * template name: MontgomeryModInt
 * author: Misuki
 * reference: https://github.com/NyaanNyaan/library/blob/master/modint/montgomery-modint.hpp#L10
 * last update: 2023/11/30
 * note: mod should be a prime less than 2^30.
 */

template<uint32_t mod>
struct MontgomeryModInt {
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 res = 1, base = mod;
    for(i32 i = 0; i < 31; i++)
      res *= base, base *= base;
    return -res;
  }

  static constexpr u32 get_mod() {
    return mod;
  }

  static constexpr u32 n2 = -u64(mod) % mod; //2^64 % mod
  static constexpr u32 r = get_r(); //-P^{-1} % 2^32

  u32 a;

  static u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * r) * mod) >> 32;
  }

  static u32 transform(const u64 &b) {
    return reduce(u64(b) * n2);
  }

  MontgomeryModInt() : a(0) {}
  MontgomeryModInt(const int64_t &b) 
    : a(transform(b % mod + mod)) {}

  mint pow(u64 k) const {
    mint res(1), base(*this);
    while(k) {
      if (k & 1) 
        res *= base;
      base *= base, k >>= 1;
    }
    return res;
  }

  mint inverse() const { return (*this).pow(mod - 2); }

  u32 get() const {
    u32 res = reduce(a);
    return res >= mod ? res - mod : res;
  }

  mint& operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  mint& operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  mint& operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  mint& operator/=(const mint &b) {
    a = reduce(u64(a) * b.inverse().a);
    return *this;
  }

  mint operator-() { return mint() - mint(*this); }
  bool operator==(mint b) {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(mint b) {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }

  friend mint operator+(mint a, mint b) { return a += b; }
  friend mint operator-(mint a, mint b) { return a -= b; }
  friend mint operator*(mint a, mint b) { return a *= b; }
  friend mint operator/(mint a, mint b) { return a /= b; }

  friend ostream& operator<<(ostream& os, const mint& b) {
    return os << b.get();
  }
  friend istream& operator>>(istream& is, mint& b) {
    int64_t val;
    is >> val;
    b = mint(val);
    return is;
  }
};

using mint = MontgomeryModInt<998244353>;

/**
 * template name: comb
 * author: Misuki
 * last update: 2023/01/22
 * note: remember to call init() before using it.
 */

const int MAX = 200001 + 50;
mint fac[MAX], facInv[MAX];
void init() {
  fac[0] = 1;
  for(int i = 1; i < MAX; i++)
    fac[i] = fac[i - 1] * i;
  facInv[MAX - 1] = 1 / fac[MAX - 1];
  for(int i = MAX - 2; i >= 0; i--)
    facInv[i] = facInv[i + 1] * (i + 1);
}

mint C(int a, int b) {
  if (b < 0 or a < b)
    return 0;
  else
    return fac[a] * facInv[b] * facInv[a - b];
}

/**
 * template name: hashTable
 * reference: https://codeforces.com/blog/entry/62393
 * last update: 2022/12/03
 * header: bit/extc++.h (or ext/pb_ds/assoc_container.hpp for CF)
 */

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

using namespace __gnu_pbds;

gp_hash_table<ll, int, custom_hash> toId;

const int pi = 40;

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  init();

  int n, m; cin >> n >> m;
  vector<mint> a(n);
  for(mint &x : a)
    cin >> x;

  vector<int> div;
  for(int i = 1; i * i <= m; i++) {
    if (m % i == 0) {
      div.emplace_back(i);
      if (i * i != m)
        div.emplace_back(m / i);
    }
  }
  R::sort(div);

  vector<int> pf;
  {
    int tmp = m;
    for(int i = 2; i * i <= m; i++) {
      if (tmp % i == 0) {
        pf.emplace_back(i);
        while(tmp % i == 0)
          tmp /= i;
      }
    }
    if (tmp != 1)
      pf.emplace_back(tmp);
  }

  for(int i = 0; i < ssize(div); i++)
    toId[div[i]] = i;

  vector<vector<int>> f(ssize(div));
  for(int i = 0; int d : div) {
    for(int p : pf) {
      if (d % p == 0) {
        f[i].emplace_back(0);
        while(d % p == 0)
          d /= p, f[i].back()++;
      }
    }
    i++;
  }

  vector<vector<array<int, 2>>> trans(ssize(div));
  for(int j = 0; j < ssize(div); j++)
    for(int k = 1; k <= j; k++)
      if (div[j] % div[k] == 0)
        trans[j].push_back({toId[div[j] / div[k]], div[k] - 1});

  vector dp(pi + 1, vector<mint>(ssize(div)));
  dp[0][0] = 1;
  for(int i = 1; i <= pi; i++)
    for(int j = 0; j < ssize(div); j++)
      for(auto [k, r] : trans[j])
        dp[i][j] += dp[i - 1][k] * r;

  vector<mint> dp2(pi + 1);
  dp2[0] = 1;
  for(int i = 0; i < n; i++) {
    vector<mint> tmp(pi + 1);
    for(int j = 0; j <= pi; j++)
      tmp[j] = dp2[j] * (a[i] + 1);
    for(int j = 1; j <= pi; j++)
      tmp[j] += dp2[j - 1];
    dp2.swap(tmp);
  }

  mint ans = 0;
  for(int i = 0; i <= min(n, pi); i++) {
    for(int j = 0; j < ssize(div); j++) {
      mint tmp = 1;
      for(int k : f[toId[m / div[j]]])
        tmp *= C(n - i - 1 + k, k);
      ans += dp[i][j] * dp2[i] * tmp;
    }
  }

  cout << ans << '\n';
/*
  cout << "div: " << div << '\n';
  cout << "pf: " << pf << '\n';
  cout << "f: " << f << '\n';
  cout << "dp: \n";
  for(auto v : dp)
    cout << v << '\n';
  cout << "dp2: " << dp2 << '\n';
  for(auto [x, y] : toId)
    cout << x << ' ' << y << '\n';
*/
  return 0;
}