#include<bits/stdc++.h>
#define LL long long
using namespace std;
const int mo=998244353;
LL m;
int n,mf,res,a[200020],fac[200020],ifac[200020],dp[200020][44],sp[200020][44];
int fcc[200020][44][44];
vector<LL> f,pf;
int ksm(int x,int y){
	int res=1;
	while (y){
		if (y&1) res=1ll*res*x%mo;
		x=1ll*x*x%mo;
		y/=2;
	}
	return res;
}
void init(){
	int maxn=200002;
	fac[0]=1;
	for (int i=1;i<=maxn;i++) fac[i]=1ll*fac[i-1]*i%mo;
	ifac[maxn]=ksm(fac[maxn],mo-2);
	for (int i=maxn;i;i--) ifac[i-1]=1ll*ifac[i]*i%mo;
	//printf("gg\n");
	return;
}
void split(){
	for (int i=1;1ll*i*i<=m;i++)
	if (m%i==0){
		f.push_back(i);
		if (m/i!=i) f.push_back(m/i);
	}
	LL tmp=m;
	for (int i=2;1ll*i*i<=m;i++)
	if (tmp%i==0){
		pf.push_back(i);
		while (tmp%i==0) tmp/=i;
	}
	if (tmp!=1) pf.push_back(tmp); 
	//for (int i=0;i<pf.size();i++) printf("%lld\n",pf[i]);
	return;
}
LL c(int x,int y){//x>=y
	if (x<y) return 0;
	return 1ll*fac[x]*ifac[y]%mo*ifac[x-y]%mo;
}
void work(){
	int num[15],fm;
	LL tmp;
	sp[0][0]=1;
	for (int i=1;i<f.size();i++){
		sp[i][1]=1;
		memset(num,0,sizeof(num));
		tmp=f[i];
		//printf("%lld\n",tmp);
		for (int j=0;j<pf.size();j++){
			while (tmp%pf[j]==0){
				tmp/=pf[j];
				//printf("%lld %lld\n",tmp,pf[j]);
				num[j]++;
			}
		}
		//printf("gg\n");
		fm=1;
		while (sp[i][fm]!=0){
			sp[i][fm+1]=1;	
			for (int j=0;j<pf.size();j++)
				sp[i][fm+1]=sp[i][fm+1]*c(num[j]+fm,fm)%mo;
			for (int j=1;j<=fm;j++)
				sp[i][fm+1]=(sp[i][fm+1]-sp[i][j]*c(fm+1,j))%mo;
			sp[i][fm+1]=(sp[i][fm+1]+mo)%mo;
			fm+=1;
			//printf("%lld %d %d\n",f[i],fm,sp[i][fm]);
		}
		fm--;
		mf=max(mf,fm);
	}
	return;
}
int main(){
	scanf("%d%lld",&n,&m);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]);
	init();
	split();
	work();
	fcc[0][0][0]=1;
	/*
	for (int i=0;i<f.size();i++){
		printf("%d:\n",f[i]);
		for (int j=1;j<=mf;j++) printf("	%d\n",sp[i][j]);
	}
	*/
	for (int i=1;i<=n;i++){
		fcc[i][0][0]=1ll*fcc[i-1][0][0]*(a[i]+1)%mo;
		for (int j=1;j<=mf;j++){
			fcc[i][j][0]=(1ll*fcc[i-1][j][0]*(a[i]+1)+1ll*fcc[i-1][j-1][0]*a[i])%mo;
			for (int k=1;k<=j;k++){
				fcc[i][j][k]=(1ll*fcc[i-1][j][k]*(a[i]+1)+1ll*fcc[i-1][j-1][k]*a[i]+1ll*fcc[i-1][j-1][k-1]*1)%mo;
			}
		}
	}
	/*
	for (int i=1;i<=n;i++){
		for (int j=0;j<=mf;j++) 
			for (int k=0;k<=j;k++) printf("%d %d %d %d\n",i,j,k,fcc[i][j][k]);
		printf("\n");
	}
	*/
	for (int i=1;i<=mf;i++){
		int tmp=0;
		tmp=1ll*fcc[n][i][0]*sp[1][i]%mo; //no pick
		//printf("%d\n",tmp);
		for (int j=1;j<=i;j++){
			/*
			for (int k=1;k<=n;k++) 
				tmp=(tmp+1ll*fcc[k-1][j-1]*c(n-k,i-j)%mo*ac[k+1]%mo)%mo;
			*/
			for (int k=0;k<f.size();k++){
				//printf("%d %d %d\n",k,j,sp[k][j]);
				//printf("%d %d %d\n",k^1,i-j,sp[k^1][i-j]);
				//printf("%lld\n",f[k]);
				if ((k^1)<f.size())
					tmp=(tmp+1ll*f[k]*sp[k][j]%mo*sp[k^1][i-j]%mo*fcc[n][i][j])%mo;
				else
					tmp=(tmp+1ll*f[k]*sp[k][j]%mo*sp[k][i-j]%mo*fcc[n][i][j])%mo;
				//printf("%d\n",tmp2);
				//printf("%lld\n",1ll*f[k]*sp[k][j]%mo*sp[k^1][i-j]%mo*fcc[n][i][j]);
			}
		}
		res=(res+tmp)%mo;
	}
	if (mf==0) res=fcc[n][0][0];
	printf("%d\n",res);
}