#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#include<vector>
#include<climits>
using namespace std;
#define ll long long
#define mod 998244353
ll n,k;
ll a[110][1010];
ll l[110];
ll ans[110];
ll maxx=-1;
ll gcd(ll x,ll y)
{
	if(y==0)
	{
		return x;
	}
	return gcd(y,x%y);
}

ll lcm(ll x,ll y)
{
	return (x*y)/gcd(x,y);
}

int main()
{
	scanf("%lld%lld",&n,&k);
	for(ll i=1;i<=n;i++)
	{
		scanf("%lld",&l[i]);
		for(int j=1;j<=l[i];j++)
		{
			scanf("%lld",&a[i][j]);
		}
		if(i==1)
			continue;
		ll bei=lcm(l[i],l[i-1]);
		if(k>bei)
		{
			ll ii=1,jj=1;
			ll bb=0;
			for(int j=1;j<=bei;j++)
			{
				if(ii>l[i-1])
					ii=1;
				if(jj>l[i])
				{
					jj=1;
				}
				bb+=(a[i-1][ii]%mod*a[i][jj]%mod)%mod;
				ii++;jj++;
			}
			ll cnt=k/bei;
			if(k%bei==0)
			{
				ans[i]=(bb%mod*cnt%mod)%mod;
				if(ans[i]>maxx)
					maxx=ans[i];
			}
			
		}
		else{
			ll ii=1,tot=0,jj=1;
			while(1)
			{
				tot++;
				if(tot>k)
					break;
				if(ii>l[i-1])
				{
					ii=1;
				}
				if(jj>l[i])
				{
					jj=1;
				}
				ans[i]+=(a[i-1][ii]%mod*a[i][jj]%mod)%mod;
				ii++;jj++;
			}
			ans[i]%=mod;
			if(ans[i]>maxx)
			{
				maxx=ans[i];
			}
		}
	}
	printf("%lld",maxx);
	return 0;
}