Codecraft-17 and Codeforces Round #391 (Div. 1 + Div. 2, combined) C. Felicity is Coming!

#include<bits/stdc++.h>

using namespace std;

#define X first
#define Y second
#define eps  1e-2
#define gcd __gcd
#define pb push_back
#define PI acos(-1.0)
#define lowbit(x) (x)&(-x)
#define bug printf("!!!!!\n");
#define mem(x,y) memset(x,y,sizeof(x))

typedef long long LL;
typedef long double LD;
typedef pair<int,int> pii;
typedef unsigned long long uLL;

const int maxn = 1e6+2;
const int INF  = 1<<30;
const int mod  = 1e9+7;

int n,m;
std::vector<int> v[maxn];

void solve(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++){
        int x,y;scanf("%d",&x);
        for(int j=1;j<=x;j++){
            scanf("%d",&y);
            v[y].push_back(i);
        }
    }
    for(int i=1;i<=m;i++) sort(v[i].begin(),v[i].end());
    sort(v+1,v+1+m);
    LL ans=1,cnt=1;
    for(int i=2;i<=m;i++){
        if(v[i]==v[i-1]){
            ++cnt;
        }else cnt=1;
        ans=ans*cnt%mod;
    }
    cout<<ans<<endl; 
    
    
    return;
}

int main()
{
//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
//    ios::sync_with_stdio(false);
    int t = 1;
    //scanf("%d",&t);
    while(t--){
    //    printf("Case %d: ",cas++);
        solve();
    }
    return 0;
}