#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;
#define rep(i, n) for (ll i = 0; i < (ll) (n); i++)
using mint = modint998244353;
using vm = vector<mint>;
using vvm = vector<vm>;
vector<mint> fact, factinv, inv;
const ll mod = 998244353;

void prenCkModp(ll n) {
    fact.resize(n + 5);
    factinv.resize(n + 5);
    inv.resize(n + 5);
    fact[0] = fact[1] = factinv[0] = factinv[1] = inv[1] = 1;
    for (ll i = 2; i < n + 5; i++) {
        fact[i] = (fact[i - 1] * i);
        inv[i] = (mod - ((inv[mod % i] * (mod / i))));
        factinv[i] = (factinv[i - 1] * inv[i]);
    }
}
mint nCk(ll n, ll k) {
    if (n < k || k < 0) return 0;
    return (fact[n] * ((factinv[k] * factinv[n - k])));
}

int main() {
    ll N,K,k=0;
    cin>>N>>K;
    vll A(N);
    rep(i,N){
        cin>>A[i];
        A[i]=gcd(A[i],K);
    }
    map<ll,ll> M;
    for(ll d=1;d*d<=K;d++)if(K%d==0)M[d]=M[K/d]=1;
    for(auto m:M)M[m.first]=k,k++;
    vll D(k,0),KP(k);
    for(auto m:M)KP[m.second]=m.first;
    rep(i,N)D[M[A[i]]]++;
    vvm DP(k+1,vm(k,0));
    prenCkModp(N+1);
    DP[0][0]=1;
    unordered_map<ll,ll> MM;
    for(auto m:M)MM[m.first]=m.second;
    vvll nx(k,vll(k));
    rep(i,k)rep(j,k)nx[i][j]=MM[gcd(K,KP[i]*KP[j])];
    vector<mint> p2(N+1,1);
    rep(i,N)p2[i+1]=p2[i]*2;
    rep(i,k)rep(j,k){
        if(DP[i][j].val()==0)continue;
        ll r=j;
        mint us=p2[D[i]];
        rep(d,D[i]+1){
            mint multi=nCk(D[i],d);
            us-=multi;
            DP[i+1][r]+=DP[i][j]*multi;
            if(r==nx[r][i])break;
            r=nx[r][i];
        }
        DP[i+1][r]+=DP[i][j]*us;
    }
    if(K==1)DP[k][k-1]-=1;
    cout<<DP[k][k-1].val()<<endl;
}