```go
package main

import (
	"bufio"
	"io"
	"os"
	"sort"
	"strconv"
)

const MOD int64 = 1000000007

type Pair struct {
	g int
	c int
}

func main() {
	data, _ := io.ReadAll(os.Stdin)
	idx := 0
	nextInt := func() int {
		n := 0
		sign := 1
		for idx < len(data) && (data[idx] < '0' || data[idx] > '9') && data[idx] != '-' {
			idx++
		}
		if idx < len(data) && data[idx] == '-' {
			sign = -1
			idx++
		}
		for idx < len(data) && data[idx] >= '0' && data[idx] <= '9' {
			n = n*10 + int(data[idx]-'0')
			idx++
		}
		return sign * n
	}

	n := nextInt()
	m := nextInt()

	typeMap := make(map[int][]Pair, 1<<16)

	for gi := 1; gi <= n; gi++ {
		cnt := nextInt()
		arr := make([]int, cnt)
		for i := 0; i < cnt; i++ {
			arr[i] = nextInt()
		}
		sort.Ints(arr)
		for i := 0; i < cnt; {
			t := arr[i]
			j := i + 1
			for j < cnt && arr[j] == t {
				j++
			}
			typeMap[t] = append(typeMap[t], Pair{g: gi, c: j - i})
			i = j
		}
	}

	sigCount := make(map[string]int, len(typeMap)+1)
	buf := make([]byte, 0, 32)
	for _, pairs := range typeMap {
		b := buf[:0]
		for _, p := range pairs {
			b = strconv.AppendInt(b, int64(p.g), 10)
			b = append(b, '#')
			b = strconv.AppendInt(b, int64(p.c), 10)
			b = append(b, ';')
		}
		key := string(b)
		sigCount[key]++
	}

	zeroClass := m - len(typeMap)
	if zeroClass > 0 {
		sigCount[""] += zeroClass
	}

	fact := make([]int64, m+1)
	fact[0] = 1
	for i := 1; i <= m; i++ {
		fact[i] = fact[i-1] * int64(i) % MOD
	}

	ans := int64(1)
	for _, cnt := range sigCount {
		ans = (ans * fact[cnt]) % MOD
	}

	w := bufio.NewWriter(os.Stdout)
	w.WriteString(strconv.FormatInt(ans, 10))
	w.WriteByte('\n')
	w.Flush()
}
```