#include<bits/stdc++.h>
using namespace std;
#define For(i,a,b) for(int i=(a);i<=(b);i++)
#define Rof(i,a,b) for(int i=(a);i>=(b);i--)
#define wln putchar('\n')
#define ll long long
#define vi vector<int> 
const int N=300005,MOD=998244353,N2=1<<17,G=3;
int sqr(int x){return 1ll*x*x%MOD;}
int mo(int x){return x>=MOD?x-MOD:x;}
void moplus(int &x,int y){x=mo(x+y);}
int ksm(int a,int b)
{
    int res=1;
    while(b)
    {
        if(b&1)res=1ll*res*a%MOD;
        a=1ll*a*a%MOD;
        b>>=1;
    }
    return res;
}
int fac[N],ifac[N];
void math_init(int n)
{
    fac[0]=1;
    For(i,1,n)fac[i]=1ll*fac[i-1]*i%MOD;
    ifac[n]=ksm(fac[n],MOD-2);
    Rof(i,n,1)ifac[i-1]=1ll*ifac[i]*i%MOD;
}
int getC(int a,int b){return 1ll*fac[a]*ifac[b]%MOD*ifac[a-b]%MOD;}
void dft(int n,int a[],int w[])
{
    for(int i=0;(1<<i)<n;i++)
        for(int j=0;j<n;j+=1<<i+1)
            For(k,0,(1<<i)-1)
            {
                int x=a[j+k],y=1ll*w[(n>>i+1)*k]*a[j+(1<<i)+k]%MOD;
                a[j+k]=mo(x+y); a[j+(1<<i)+k]=mo(x-y+MOD);
            }
}
void mul(int n,int a[],int b[])
{
    static int r[N2],w[N2>>1];
    int invn=ksm(n,MOD-2);
    r[0]=0;
    For(i,1,n-1)
    {
        r[i]=r[i>>1]>>1|(i&1)*(n>>1);
        if(r[i]<i)swap(a[r[i]],a[i]),swap(b[r[i]],b[i]);
    }
    w[0]=1; w[1]=ksm(G,(MOD-1)/n);
    For(i,2,(n>>1)-1)w[i]=1ll*w[i-1]*w[1]%MOD;
    dft(n,a,w); dft(n,b,w);
    For(i,0,n-1)
    {
        a[i]=1ll*a[i]*b[i]%MOD;
        if(r[i]<i)swap(a[r[i]],a[i]);
    }
    dft(n,a,w);
    reverse(a+1,a+n);
    For(i,0,n-1)a[i]=1ll*a[i]*invn%MOD;
}
void mul(vi &a,vi &b)
{
    int lena=a.size(),lenb=b.size(),n=1;
    while(n<lena+lenb-1)n<<=1;
    int aa[n],bb[n];
    copy(a.begin(),a.end(),aa);
    copy(b.begin(),b.end(),bb);
    fill(aa+lena,aa+n,0);
    fill(bb+lenb,bb+n,0);
    mul(n,aa,bb);
    while(n&&aa[n-1]==0)n--;
    a.clear();
    For(i,0,n-1)a.push_back(aa[i]);
}
int n,a[N],lenp;
vi A[N];
ll m,p[N];
void solve(int l,int r)
{
    if(l==r)return;
    int mid=l+r>>1;
    solve(l,mid);
    solve(mid+1,r);
    mul(A[l],A[mid+1]);
}
int main()
{
    math_init(300000);
    scanf("%d%lld",&n,&m);
    ll mm=m;
    for(int i=2;1ll*i*i<=m;i++)
        if(m%i==0)
        {
            p[++lenp]=i;
            while(m%i==0)m/=i,a[lenp]++;
        }
    if(m>1)p[++lenp]=m,a[lenp]=1;
    //For(i,1,lenp)printf("(%lld,%d)",p[i],a[i]); wln;
    m=mm;
    For(i,1,n)
    {
        int x;
        scanf("%d",&x);
        A[i].push_back(x);
        A[i].push_back(1);
    }
    solve(1,n);
    //for(int x:A[1])printf("%d ",x); wln;
    //printf("---\n");
    int res=(m+A[1][0])%MOD;
    For(i,1,lenp)res=1ll*res*getC(a[i]+n-1,n-1)%MOD;
    //printf("res=%d\n",res);
    For(i,1,n-1)
    {
        int s=A[1][i];
        For(j,1,lenp)
        {
            int ss=0,x=1;
            For(k,0,a[j])
            {
                ss=(ss+1ll*x*getC(k+i-1,i-1)%MOD*getC(a[j]-k+n-i-1,n-i-1))%MOD;
                x=1ll*x*p[j]%MOD;
            }
            s=1ll*s*ss%MOD;
        }
        moplus(res,s);
    }
    printf("%d",res);
}