You may know that Euclid was a mathematician. Well, as it turns out, Morpheus knew it too. So when he wanted to play a mean trick on Euclid, he sent him an appropriate nightmare. 

In his bad dream Euclid has a set S of n m-dimensional vectors over the Z_2 field and can perform vector addition on them. In other words he has vectors with m coordinates, each one equal either 0 or 1. Vector addition is defined as follows: let u+v = w, then w_i = (u_i + v_i) mod 2. 

Euclid can sum any subset of S and archive another m-dimensional vector over Z_2. In particular, he can sum together an empty subset; in such a case, the resulting vector has all coordinates equal 0.

Let T be the set of all the vectors that can be written as a sum of some vectors from S. Now Euclid wonders the size of T and whether he can use only a subset S' of S to obtain all the vectors from T. As it is usually the case in such scenarios, he will not wake up until he figures this out. So far, things are looking rather grim for the philosopher. But there is hope, as he noticed that all vectors in S have at most 2 coordinates equal 1. 

Help Euclid and calculate |T|, the number of m-dimensional vectors over Z_2 that can be written as a sum of some vectors from S. As it can be quite large, calculate it modulo 10^9+7. You should also find S', the smallest such subset of S, that all vectors in T can be written as a sum of vectors from S'. In case there are multiple such sets with a minimal number of elements, output the lexicographically smallest one with respect to the order in which their elements are given in the input. 

Consider sets A and B such that |A| = |B|. Let a_1, a_2, ... a_{|A|} and b_1, b_2, ... b_{|B|} be increasing arrays of indices elements of A and B correspondingly. A is lexicographically smaller than B iff there exists such i that a_j = b_j for all j < i and a_i < b_i.

Input

In the first line of input, there are two integers n, m (1 ≤ n, m ≤ 5 ⋅ 10^5) denoting the number of vectors in S and the number of dimensions. 

Next n lines contain the description of the vectors in S. In each of them there is an integer k (1 ≤ k ≤ 2) and then follow k distinct integers x_1, ... x_k (1 ≤ x_i ≤ m). This encodes an m-dimensional vector having 1s on coordinates x_1, ... x_k and 0s on the rest of them.

Among the n vectors, no two are the same.

Output

In the first line, output two integers: remainder modulo 10^9+7 of |T| and |S'|. In the second line, output |S'| numbers, indices of the elements of S' in ascending order. The elements of S are numbered from 1 in the order they are given in the input.

Examples

Input


3 2
1 1
1 2
2 2 1


Output


4 2
1 2 


Input


2 3
2 1 3
2 1 2


Output


4 2
1 2 


Input


3 5
2 1 2
1 3
1 4


Output


8 3
1 2 3 

Note

In the first example we are given three vectors: 

  * 10 
  * 01 
  * 11 



It turns out that we can represent all vectors from our 2-dimensional space using these vectors: 

  * 00 is a sum of the empty subset of above vectors; 
  * 01 = 11 + 10, is a sum of the first and third vector; 
  * 10 = 10, is just the first vector; 
  * 11 = 10 + 01, is a sum of the first and the second vector. 



Hence, T = \{00, 01, 10, 11\}. We can choose any two of the three vectors from S and still be able to obtain all the vectors in T. In such a case, we choose the two vectors which appear first in the input. Since we cannot obtain all vectors in T using only a single vector from S, |S'| = 2 and S' = \{10, 01\} (indices 1 and 2), as set \{1, 2 \} is lexicographically the smallest. We can represent all vectors from T, using only vectors from S', as shown below: 

  * 00 is a sum of the empty subset; 
  * 01 = 01 is just the second vector; 
  * 10 = 10 is just the first vector; 
  * 11 = 10 + 01 is a sum of the first and the second vector. 
/*
                                                                                                     
                                             `-:://:::-                                             
                                           `//:-------:/:`                                          
                                          .+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .o:--...```..---+/`                                        
                                       `/y+o/---....---:+o.                                         
                                   `...````-os+/:---:/+o/--.`                                       
              `-/+++++/:.      `...`       :h+d+oooo+/+-`   ...                                     
            `/++//:::://++-`....`         -.`//````````:`     `..`                                  
           `o+/::------://o/`           `-` -.          -`       `..`                               
 `---.-o/:./o/::-..``..-ЗАПУСКАЕМ      ..  ..            -`        `...       ``..``                
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          `:s+/:--....-::/+s-`      .-   `-                -`           -///:--------:/:`           
           ./s+//:::::://oo-``..НЕЙРОННУЮ: СЕТЬ:::::::-`РАБОТЯГИ        `+:--........--:/`          
            .:ooo+++++osso-`    `.:-...`/` ./::-------:/:`   -`         :+--..``````.--:+:...-+:-`  
             `.-/+++++/+-.-`    -.   ``:so:/:--.......--:+`  `-```````o+/+--..`````..--:o/-..:s+:.  
                 ```````:``.. `-`     -` `+:--..`````..--/+-.../.`````..-o:--.......---/o.    `     
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                         `-`-...    ..   .o/--...```..--:+/`    `-`     `oy/so/////++o/.`           
                          -/`  `-` `- ``+s/o/:---...---:++.      `-`   .-../d://///:-.`             
                `.---..``-..-    .-/..`````-oo+/:::::/+o+-        `-``-`  `-.  ````                 
             `:++++/+++++-  ..``.-/:`      /y-:/++o++/:.`..`       ./.   `-                         
            -++/::::::://+/..:-``:` ..   `-.`  ```.```    `..`   `..`-` `-                          
       ``  -o//:--....-::/++` -.-`   `-`.-`                 `..`..`  `-.-                           
  -----ss+:++/:--.```..-://s.  /.     `::                    `-:.     ./`                           
  `````/:..+o/::-..``.--:/+s. ..-`   `-``-`                 ..` `-`  `-`-`                          
          `-s+/::-----::/+oo---``-` ..    .:-    ```      .-`     .-.-  `-`                         
           `:oo+//::://+os/..:`..-/:`      :y.-:::::::.`.-`        ./-`  `-`                        
            `./+oooooooo+/.`-    .-:...`.. .//:-------://`        `- `..` `:.                       
              ``.-::::-.``-/`  `-` `-  `oo:+:--.......--:/`      `-    `.:--h.``..```               
                          -.-`.-    .-   `+:--..`````..--//`    `-       /s-//::::::::.             
                         -` `/-      ..  .o:--..`` ``..--:o.```.-        `//:--------://`           
                        -` .-`.-`     -.`-o/--...```..--:+/.``-:....``:-.+:--....`...--:+`          
                       ..`-.   `-.   ``:os:o/:---...---:++.  `-     ``///+:-..``````.--:+-````-.`   
              `.:///////.-`      .:-..` -``-+o+/:::::/+o/.  `-         `:+:-..`````..--:o/:--/ys+-  
            `-++///////+o/. ``....`-.    :` `.:++++++/:.`  .-           -o/---......---/o.   `.`    
           `++//:-----::/+o:..`     .-`   :    ```````    .-           `+so+:--------:++-`          
  `````:-``:o/::-..`..--:/+o`         -.  `-             .-          `../../+o+////+o+:.`           
  -----syo/o+/:--.```..-://s.          .-` `-           .-        `...     ``-:////:-``             
       .` `/s//:--....-::/+s.            -. `-`        .-       `..`                                
           .+o+/:::--:://+s/-..`          .::+y  ```  .-     `..`                                   
            ./oo++////+oso-`   `....       :y-+:::::::/`   ...                                      
             `.:+oooooo/-`         `....-. .//:-------:/:-.`                                        
                ``...``                 /+:+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .+/--...```..--:+/`                                        
                                         `-o/:---...---:++.                                         
                                          `-+o+/:---:/+o/.                                          
                                            `.:+oooo+/-.`                                           
                                               ``````                                               
*/

#ifdef aimbot
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")
#endif

#define hur(f, g) template<class c> int f(c a) {if (sizeof(c) == 8) return g##ll(a); else return g(a);}
hur(popc, __builtin_popcount) hur(ctz, __builtin_ctz) hur(clz, __builtin_clz)

/*
	- place bitset modifications here
*/

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <set>
#include <queue>
#include <ostream>
#include <istream>
#include <typeinfo>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <cassert>
#include <limits>
#include <fstream>
#include <array>
#include <list>
#include <bitset>
#include <functional>
#include <random>
#include <cstring>
#include <chrono>

#define random escape__from__random__aetuhoetnuhshe
#define mt make_tuple
#define x first
#define y second
#define pb push_back
#define mp make_pair
#define le(v) ((int)v.size())
#define f(i, n) for (int i = 0; i < (n); i++)
#define rof(i, n) for (int i = ((n) - 1); i >= 0; i--)
#define apply(v, act) for (auto &x : v) { act; }
#define log(args...) {string s = #args;deque<string> deq;\
string buf = "";int bal = 0;for (char c : s) {\
if (c == '(' || c == '[' || c == '{') {bal++;\
} else if (c == ')' || c == ']' || c == '}') {\
bal--;} else {if (bal == 0) {if (c == ',') {\
deq.pb(buf);buf = "";} else {if (c != ' ') {\
buf += c;}}}}}if (!buf.empty()) {deq.pb(buf);}\
smart_io::precall_print();smart_io::_print(deq, args);}

inline int min(const int &x, const int &y) { return (((y-x)>>(32-1))&(x^y))^x; }
inline int max(const int &x, const int &y) { return (((y-x)>>(32-1))&(x^y))^y; }
inline long long min(const long long &x, const long long &y) { return (((y-x)>>(64-1))&(x^y))^x; }
inline long long max(const long long &x, const long long &y) { return (((y-x)>>(64-1))&(x^y))^y; }

#define print    \
smart_io::precall_print(); \
cout,

#define scan cin,

#ifdef fast_allocator
const int MAXMEM = 200 * 1000 * 1024;
char _memory[MAXMEM];
size_t _ptr = 0;
void* operator new(size_t _x) { _ptr += _x; assert(_ptr < MAXMEM); return _memory + _ptr - _x; }
void operator delete (void*) noexcept {}
#endif

using namespace std;

char string_in_buffer[(int)260];


void fast_scan(int &x) { scanf("%d", &x); }
void fast_scan(long long &x) { scanf("%lld", &x); }
void fast_scan(unsigned long long &x) { scanf("%llu", &x); }
void fast_scan(double &x) { scanf("%lf", &x); }
void fast_scan(long double &x) { scanf("%Lf", &x); }
void fast_scan(char &x) {
	scanf("%c", &x);
	if (x == '\n') {
		fast_scan(x);
	}
}
void fast_scan(string &x) {
	scanf("%s", string_in_buffer);
	x = string(string_in_buffer);
}

template<class TFirst, class TSecond>
void fast_scan(pair<TFirst, TSecond> &p) {
	fast_scan(p.first);
	fast_scan(p.second);
}

template <class T>
void fast_scan(vector<T> &v) {
	for (auto &x : v) fast_scan(x);
}

void fast_print(const int &x) { printf("%d", x); }
void fast_print(const unsigned int &x) { printf("%u", x); }
void fast_print(const long long &x) { printf("%lld", x); }
void fast_print(const unsigned long long &x) { printf("%llu", x); }
void fast_print(const char &x) { printf("%c", x); };
// void fast_print(__int128 x) {
// 	if (x == 0) { fast_print('0'); return; }
// 	if (x < 0) {
// 		fast_print('-');
// 		x = -x;
// 	}
// 	__int128 p = 1;
// 	while (x / (p * 10)) p *= 10;
// 	while (p) {
// 		__int128 symb = x / p;
// 		fast_print((int)symb);
// 		x -= p * symb;
// 		p /= 10;
// 	}
// };
void fast_print(const double &x) { printf("%.15lf", x); }
void fast_print(const long double &x) { printf("%.15Lf", x); }
void fast_print(const string &x) { printf("%s", x.c_str());}
void fast_print(const char v[]) { fast_print((string)v); }

template<class TFirst, class TSecond>
void fast_print(const pair<TFirst, TSecond> &p) {
	fast_print(p.first);
	fast_print(' ');
	fast_print(p.second);
}

template <class T>
void fast_print(const vector<T> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print(' ');
		fast_print(v[i]);
	}
}

template <class T>
void fast_print(const vector<vector<T>> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print('\n');
		fast_print(v[i]);
	}
}

template <class T>
void fast_print(const T &v) {
	for (const auto &x : v) {
		fast_print(x);
		fast_print(' ');
	}
}


using namespace std;


namespace smart_io {
	string print_start = "";
	string sep = " ";
	bool first_print = false;
	
	void precall_print() {
		fast_print(print_start);
		print_start = "\n";
		first_print = true;
	}
	
	void _print(deque<string>) {}
	template<class T, class... Args>
	void _print(deque<string> names, T elem, Args... args) {
		if (!first_print) {
			fast_print("\n");
		} else {
			first_print = false;
		}
		fast_print(names.front());
		fast_print(" = ");
		fast_print(elem);
		names.pop_front();
		_print(names, args...);
	}
} //namespace smart_io


template <class T>
ostream &operator,(ostream &os, const T &object) {
	if (!smart_io::first_print) {
		fast_print(smart_io::sep);
	} else {
		smart_io::first_print = false;
	}
	fast_print(object);
	return os;
}

template <class T>
istream &operator,(istream &is, T &object) {
	fast_scan(object);
	return is;
}

namespace random {
	using namespace std::chrono;
	mt19937 rng(duration_cast< milliseconds >(
											  system_clock::now().time_since_epoch()
											  ).count());
	uniform_real_distribution<> prob_dist(0.0, 1.0);
};

namespace typedefs {
	typedef long long ll;
	typedef unsigned long long ull;
	typedef pair<int, int> pii;
	typedef long double ld;
}

namespace numbers_operation {
	template<class T>
	inline T floor_mod(T a, const T &b) {
		a %= b;	
		if (a < 0) a += b;
		return a;
	}
}

using namespace numbers_operation;
using namespace typedefs;
using namespace random;

const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
template<ll MOD>
struct Ring {
	ll value = 0;
	Ring() {}
	Ring(int _value) {
		value = _value;
		value = floor_mod(value, MOD);
	}
	Ring(ll _value) {
		value = _value;
		value = floor_mod(value, MOD);
	}
	Ring pow(ll p) const {
		Ring r = 1;
		Ring x; x.value = value;
		while (p) {
			if (p & 1) r *= x;
			x *= x;
			p /= 2;
		}
		return r;
	}
	Ring inv() const {
		return pow(MOD - 2);
	}
	void operator*=(const Ring<MOD> &b) {
		value *= b.value;
		value = floor_mod(value, MOD);
	}
	friend Ring operator*(Ring<MOD> a, const Ring<MOD> &b) {
		a *= b;
		return a;
	}
	void operator+=(const Ring<MOD> &b) {
		value += b.value;
		value -= (value >= MOD) * MOD;
	}
	friend Ring operator+(Ring a, const Ring &b) {
		a += b;
		return a;
	}
	void operator-=(const Ring<MOD> &b) {
		value -= b.value;
		value += (value < 0) ? MOD : 0;
	}
	friend Ring operator-(Ring a, const Ring &b) {
		a -= b;
		return a;
	}
	void operator/=(const Ring<MOD> &b) {
		(*this) *= b.inv();	
	}
	friend Ring operator/(Ring a, const Ring &b) {
		a /= b;
		return a;
	}
	bool operator==(const Ring<MOD> &b) {
		return value == b.value;
	}
	bool operator!=(const Ring<MOD> &b) {
		return value != b.value;
	}
	friend void fast_print(const Ring<MOD> &b) {
		fast_print(b.value);
	}
};

typedef Ring<MOD> num;

int n, m;
vector<int> up;
vector<bool> one;
int get_root(int v) {
	if (up[v] == v) return v;
	return up[v] = get_root(up[v]);
}
signed main(signed argc, char *argv[]) {
	scan n, m;
	up.resize(m);
	one.resize(m);
	iota(up.begin(), up.end(), 0);
	vector<int> pick;
	f(i, n) {
		int k; scan k;
		vector<int> cords(k);
		scan cords;
		apply(cords, x--)
		if (k == 1) {
			int top = get_root(cords[0]);
			if (!one[top]) {
				one[top] = true;
				pick.pb(i + 1);
			}
		} else if (k == 2) {
			int a = get_root(cords[0]);
			int b = get_root(cords[1]);
			if (a != b && !(one[a] && one[b])) {
				if (one[b]) {
					one[a] = true;
				}
				up[b] = a;
				pick.pb(i + 1);
			}
		}
	}
	print num(2).pow(le(pick)), le(pick);
	print pick;
}
