#include<bits/stdc++.h>
#define pq priority_queue
using namespace std;
const int N=1e4+5;
const int mod=998244353;
int n,w,ccf,ans=1;
int a[N],cnt[N];
pq<int,vector<int>,greater<int> >q;
int read() {
	int x = 0, y = 1;
	char ch = 0;
	while (ch < '0' || ch > '9') {
		if (ch == '-') y = -1;
		ch = getchar();
	}
	while(ch>='0' && ch<='9'){
		x=x*10+(ch-'0');
		ch=getchar();
	}
	return x*y;
}
void solve(int x,int sum) {
	for(int i=1; i<=n; i++) {
		cnt[i]=1;
		while(a[i]%x==0) cnt[i]++,a[i]/=x;
		q.push(cnt[i]);
	}
	while(sum) {
		int x=q.top();
		q.pop();
		q.push(x+1),sum--;
	}
	for(int i=1; i<=n; i++) ans=ans*q.top()%mod,q.pop();
}
int main() {
	n=read();
	w=read();
	for(int i=1; i<=n; i++) {
		a[i]=read();
	}
	for(int i=2; i*i<=w; i++) {
		if(w%i==0) {
			ccf=0;
			while(w%i==0)ccf++,w/=i;
			solve(i,ccf);
		}
	}
	if(w>1)solve(w,1);
	for(int i=1; i<=n; i++){
		for(int j=2;j*j<=a[i];j++) {
			ccf=1;
			while(a[i]%j==0)a[i]/=j,ccf++;
			ans=ans*ccf%mod;
		}
		if(a[i]>1)ans=ans*2%mod;
	}
	printf("%lld",ans);
	return 0;
}