#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define X first
#define Y second
#define ALL(v) v.begin(), v.end()
#define pb push_back
#define SZ(a) ((int)a.size())

const int MOD = 998244353;
const int L = 40;

void add(int &x, int val) {
    x += val;
    if (x >= MOD) x -= MOD;
}

int arr[200005];
int dp[2][L][L];
int C[5 * L][5 * L];

int H(int n, int m) {
    if (n + m - 1 < m) return 0;
    return C[n + m - 1][m];
}

int cal(const vector<int> &buk, int k) {
    if (buk.empty()) return k == 0;
    if (k == 0) return buk.empty();
    int sum = 0;
    for (int j : buk)
        sum += j;
    if (k > sum) return 0;
    int res = 0;
    for (int i = 0; i < k; ++i) {
        int cur = 1;
        for (int j : buk)
            cur = (ll)cur * H(k - i, j) % MOD;
        cur = (ll)cur * C[k][i] % MOD;
        if (i & 1) add(res, MOD - cur);
        else add(res, cur);
    }
    return res;
}

int main() {
    ios::sync_with_stdio(0), cin.tie(0);
    int n;
    ll m;
    cin >> n >> m;
    for (int i = 1; i <= n; ++i)
        cin >> arr[i];
    C[0][0] = 1;
    for (int i = 1; i < 5 * L; ++i) {   
        C[i][0] = 1;
        for (int j = 1; j <= i; ++j) {
            C[i][j] = C[i - 1][j];
            add(C[i][j], C[i - 1][j - 1]);
        }
    }
    vector<ll> p;
    {
        ll x = m;
        for (ll i = 2; i * i <= x; ++i)
            if (x % i == 0) {
                p.pb(i);
                while (x % i == 0) x /= i;
            }
        if (x > 1) p.pb(x);
    }
    vector<ll> fac;
    for (ll i = 1; i * i <= m; ++i)
        if (m % i == 0) {
            fac.pb(i);
            if (i * i != m) fac.pb(m / i);
        }
    dp[0][0][0] = 1;
    int prv = 0, nxt = 1;
    for (int i = 1; i <= n; ++i) {
        memset(dp[nxt], 0, sizeof(dp[nxt]));
        for (int j = 0; j < L; ++j)
            for (int k = 0; k < L; ++k)
                if (dp[prv][j][k]) {
                    add(dp[nxt][j + 1][k], dp[prv][j][k]); 
                    add(dp[nxt][j][k + 1], (ll)dp[prv][j][k] * arr[i] % MOD);
                    add(dp[nxt][j][k], (ll)dp[prv][j][k] * (arr[i] + 1) % MOD);
                }
        swap(prv, nxt);
    }
    int ans = 0;
    for (ll x : fac) {
        vector<int> buk, ibuk;
        for (ll j : p) {
            ll cur = x;
            if (cur % j == 0) {
                buk.pb(0);
                while (cur % j == 0) cur /= j, ++buk.back();
            }
            cur = m / x;
            if (cur % j == 0) {
                ibuk.pb(0);
                while (cur % j == 0) cur /= j, ++ibuk.back();
            }
        }
        vector<int> mth, imth;
        for (int j = 0; j < L; ++j) {
            mth.pb(cal(buk, j));
            imth.pb(cal(ibuk, j));
        }
        int cur = 0;
        for (int j = 0; j < L; ++j)
            for (int k = 0; k < L; ++k) {
                add(cur, (ll)dp[prv][j][k] % MOD * mth[j] % MOD * imth[k] % MOD);
            }
        add(ans, (ll)cur * (x % MOD) % MOD);
        //cerr << x << ": " << cur << "\n";
    }
    vector<int> buk;
    for (ll j : p) {
        ll cur = m;
        if (cur % j == 0) {
            buk.pb(0);
            while (cur % j == 0) cur /= j, ++buk.back();
        }
    }

    int mul = 1;
    for (int i = 1; i <= n; ++i)
        mul = (ll)mul * arr[i] % MOD;

    for (int k = 1; k < L; ++k)
        add(ans, (ll)cal(buk, k) * mul % MOD);

    
    int cnt = 1;
    for (int j : buk)
        cnt = (ll)cnt * (j + 1) % MOD;
    cnt -= 1;

    add(ans, MOD - (ll)mul * cnt % MOD);

    cout << ans << "\n";


}