#include <bits/stdc++.h>
#include <atcoder/all>
using namespace atcoder;
using mint = modint998244353;
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)

struct combi{
	deque<mint> kaijou;
	deque<mint> kaijou_;
	
	combi(int n){
		kaijou.push_back(1);
		for(int i=1;i<=n;i++){
			kaijou.push_back(kaijou[i-1]*i);
		}
		
		mint b=kaijou[n].inv();
		
		kaijou_.push_front(b);
		for(int i=1;i<=n;i++){
			int k=n+1-i;
			kaijou_.push_front(kaijou_[0]*k);
		}
	}
	
	mint combination(int n,int r){
		if(r>n)return 0;
		mint a = kaijou[n]*kaijou_[r];
		a *= kaijou_[n-r];
		return a;
	}
	
	mint junretsu(int a,int b){
		mint x = kaijou_[a]*kaijou_[b];
		x *= kaijou[a+b];
		return x;
	}
	
	mint catalan(int n){
		return combination(2*n,n)/(n+1);
	}
	
};

int main() {
    
	int N,K;
	cin>>N>>K;
	
	vector<long long> y;
	for(long long i=1;i*i<=K;i++){
		if(K%i==0){
			y.push_back(i);
			if(i*i!=K)y.push_back(K/i);
		}
	}
	sort(y.begin(),y.end());
	vector<long long> c(y.size());
	rep(i,N){
		long long a;
		cin>>a;
		a = gcd(a,K);
		c[distance(y.begin(),lower_bound(y.begin(),y.end(),a))]++;
	}
	
	vector<mint> dp(y.size());
	dp.back() = 1;
	combi C(1000000);
	rep(i,y.size()){
		
		vector<mint> cnt(30);
		vector<long long> v(30);
		long long cur = 1;
		rep(j,c[i]+1){
			cnt[min(29,j)] += C.combination(c[i],j);
			v[j] = cur;
			cur *= y[i];
			cur = gcd(cur,K);
		}
		vector<mint> ndp(y.size());
		rep(j,y.size()){
			rep(k,30){
				int d = distance(y.begin(),lower_bound(y.begin(),y.end(),y[j] / gcd(y[j],v[k])));
				ndp[d] += dp[j] * cnt[k];
			}
		}
		swap(dp,ndp);
	}
	
	cout<<dp[0].val()<<endl;
		
	
	return 0;
}