Problem: You are given an undirected graph with n vertices and m edges. Also, you are given an integer k.

Find either a clique of size k or a non-empty subset of vertices such that each vertex of this subset has at least k neighbors in the subset. If there are no such cliques and subsets report about it.

A subset of vertices is called a clique of size k if its size is k and there exists an edge between every two vertices from the subset. A vertex is called a neighbor of the other vertex if there exists an edge between them.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. The next lines contain descriptions of test cases.

The first line of the description of each test case contains three integers n, m, k (1 ≤ n, m, k ≤ 10^5, k ≤ n).

Each of the next m lines contains two integers u, v (1 ≤ u, v ≤ n, u ≠ v), denoting an edge between vertices u and v.

It is guaranteed that there are no self-loops or multiple edges. It is guaranteed that the sum of n for all test cases and the sum of m for all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case: 

If you found a subset of vertices such that each vertex of this subset has at least k neighbors in the subset in the first line output 1 and the size of the subset. On the second line output the vertices of the subset in any order.

If you found a clique of size k then in the first line output 2 and in the second line output the vertices of the clique in any order.

If there are no required subsets and cliques print -1.

If there exists multiple possible answers you can print any of them.

Example

Input


3
5 9 4
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
10 15 3
1 2
2 3
3 4
4 5
5 1
1 7
2 8
3 9
4 10
5 6
7 10
10 8
8 6
6 9
9 7
4 5 4
1 2
2 3
3 4
4 1
1 3


Output


2
4 1 2 3 
1 10
1 2 3 4 5 6 7 8 9 10 
-1

Note

In the first test case: the subset \{1, 2, 3, 4\} is a clique of size 4.

In the second test case: degree of each vertex in the original graph is at least 3. So the set of all vertices is a correct answer.

In the third test case: there are no cliques of size 4 or required subsets, so the answer is -1.

Solution (in JAVA):

Solution:
// No sorcery shall prevail. //           
import java.util.*;
import java.io.*;
public class _InVoker_ {
	//Variables
	static long mod2 = 1000000007;
	static long mod = 998244353;
	static FastReader inp= new FastReader();
	static PrintWriter out= new PrintWriter(System.out);
	public static void main(String args[]) {		    	
	   	_InVoker_ g=new _InVoker_();
	   	g.main();
	   	out.close();
	}
	
	
	
	//Main
	void main() {
		
		int t=inp.nextInt();
		loop:
		while(t-->0) {
			int n=inp.nextInt();
			int m=inp.nextInt();
			int k=inp.nextInt();
			HashSet<Integer> edges[]=new HashSet[n];
			for(int i=0;i<n;i++) edges[i]=new HashSet<>();
			Vertex nodes[]=new Vertex[n];
			for(int i=0;i<n;i++) nodes[i]=new Vertex(i);
			for(int i=0;i<m;i++) {
				Vertex x=nodes[inp.nextInt()-1];
				Vertex y=nodes[inp.nextInt()-1];
				x.list.add(y);
				y.list.add(x);
				x.deg++;
				y.deg++;
				edges[x.idx].add(y.idx);
				edges[y.idx].add(x.idx);
			}
			if((k*(k-1))/2>m) {
				out.println(-1);
				continue loop;
			}
			TreeSet<Vertex> set=new TreeSet<>();
			for(int i=0;i<n;i++) set.add(nodes[i]);
			Vertex near[]=new Vertex[n];
			while(!set.isEmpty()) {
				Vertex cur=set.pollFirst();
				if(cur.deg>=k) {
					set.add(cur);
					out.println(1+" "+set.size());
					for(Vertex x: set) out.print((x.idx+1)+" ");
					out.println();
					continue loop;
				}
				int c=0;
				cur.deleted=true;
				for(Vertex x: cur.list) {
					if(x.deleted) continue;
					if(x.deg>=k-1) {
						near[c++]=x;
					}
					set.remove(x);
					x.deg--;
					set.add(x);
				}
				if(c==k-1) {
					boolean clique=true;
					for(int i=0;i<k-1 && clique;i++) {
						for(int j=0;j<i;j++) {
							if(!edges[near[i].idx].contains(near[j].idx)) {
								clique=false;
								break;
							}
						}
					}
					if(clique) {
						out.println(2);
						out.print(cur.idx+1);
						for(int i=0;i<c;i++) out.print(" "+(near[i].idx+1));
						out.println();
						continue loop;
					}
				}
			}
			out.println(-1);
		}
		
	}
	
	long LONG_TO_INT_MASK = (1L << 32) - 1;
	long hash(int x, int y) {
		if(x>y) {
			int temp=x;
			x=y;
			y=temp;
		}
		return (((long) x) << 32) | (((long) y) & LONG_TO_INT_MASK);
	}
	
	class Vertex implements Comparable<Vertex>{
		int idx,deg;
		ArrayList<Vertex> list;
		boolean deleted=false;
		Vertex(int i){
			this.idx=i;
			deg=0;
			list=new ArrayList<>();
		}
		public int compareTo(Vertex o) {
			return deg==o.deg?Integer.compare(idx, o.idx):Integer.compare(deg, o.deg);
		}
	}
	
	
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	 *jjt.              f.:::::::::,,,,fEEKKWWWWWKKKKKWWWWWWWWWWW###WW##WKKWWWWWW#WKKKKK;.jt........i.............................:::::::;j;;....:E.KKKWWWWWWWKWW#####W#WWWWKKLLGWEEGGGGGLGGGGGGGGGGGGGGGGGGGG *
	 *jjt.             ...:::::::,,,,,;DEEKWWWWWKKKKKWWWWWWWWWWWW####WWWKKKWWWWWWWWKKKKK;.E;.........t.............................:::::ii;;.....D...KKWWWWWWWKWW#####WWEWWWKKGGGEKKGGGGGLGGGGGGGGGGGGGLGGGGGG *
	 *fji.             ;.:::::::,,,,,;LEEKKWWWWWKKKKKWWWWWWWWWWWW####KWKKKKWWWWWWWWKKKKKi.D;..........j.............................:::tt;,.....:.....KKWWWWWWKWWWW##WWWGWWWKKGGGGKEGGGGGGGGGGGGGGGGGGGLLGGGGL *
	 *fji.            t::::::::,,,,,,;EEEKWWWWWKKKKKKKWWWWWWWWWWW##WKWKKKKKWWWWWWWWKKKKKi:D;............j...........................::LL;,.............KKWWWWWKWWWWWWWWWGWWWKKGGGGKGGGGGGGGGGGGGGGGGGGGLLGGGGL *
	 *fjt:            .:::::::,,,,,,,DEEKWWWWWWKKKKKKKWWWWWWWWWWWWKKWKKKKKKWWWWK#WWKKKKWitE;........... ............................:G;;:...............KKKWWKKWWWWWWWWWGWWWKKGGGGWGGGGGGGGGGGGGGGGGGGGGGGGGGL *
	 *fjji;:.       .f:::::::,,,,,,,;EEEKWWWWWWKKKKKKWWWWWWWWWWWKKKKKKKKKKKWWKWWWWWKKKKWGKD;........................................L;;..................DKKWKKWWWWWWWWWGWWWKKDGGGKDGGGGGGGGGGGGGGGGGGGGGGGGGG *
	 *fjjtii;,:.     :::::::,,,,,,,;EEEKWWWWWWKKKKKKWWWWWWWWWWKKKKKKKKKKKKWWWWWW#WWKKKKWiEj;......................................:i,;....,...............;KKEKWWWWWWWWWGKWWKKDDGGDEGGGDGGGGGDGGGGGGGGGGGGGGGG *
	 *fjtiiiii;;:.  j::::::,,,,,,,;;EEEKWWWWW#KKKKKWWWWWWWWWKKKKKKWKKKKKKKWWWWWWWWWKKKKWtEL;:....................................;;;:...,;j................:KEEWWWWWWWWWDDWWKKDDDDDKDDDDDDDDDDDDDDDGGGGGGGGGGG *
	 *fjti;;iiii;;,:::::::,,,,,,,,;EEEKWWWWWWWKKKKWWWWWWWWKKKKKKKWKKKKKKKWWWWWWW#W#KKKKWEEii;...................................f;:....,;L...................EEKWWWWWWWWDDWWKKDDDDDKEDDDDDDDDDDDDDDDDDDDDDGGGG *
	 *fjt,,,;;;;ii;f::::::,,,,,,,;;EEKWWWWWWWKKKKKWWWKWWKKKKKKKKKKKKKKKKKWWWWWWW#W#KKKKWKEij;:...............................:G;,.....,;f....................:tKKWWWWWWWDDWWKKDDDDDKKDDDDDDDDDDDDDDDDDDDDDDDDD *
	 *jjt. ..:,;;;;,::::,,,,,,,,;;GEEWWWWWWWWKKKKWKKWKKKKKKKKKKKKKKKKKKKKWWWWWWW#W#KKKKWEDi;j;............................,Li;L;;;..,;;f........................KKKKWWWKDDWWKKDDDGDKKGGGGGGGGDGDDDDDDDDDDDDDDD *
	 *fjt.    .:,,,:::::,,,,,,,;;;EEKWWWWWWWKKKKKKWKKKKKKKKKKKKKKKKKKKKKWKKKWKW##W#KKKKWEti;;G;........................tEEEL;;;;;;;;;;L..........................DKKKKKEDDWWKEDGftiLE;;;;itjLGGGGGGDDDDDDDDDDD *
	 *fjt.       .j::::,,,,,,,;;;DEEWWWWWWWWKKKKWKKKKKKKKKKKKKKKKKKKKKKKWKKWWWK##W#KKKKKEii;;;L;...................iDEEEEEEKKi;j;;;;jD.....:......................,KKKKDGGEKKE:::::;E::::::::::,tLGGDDDDDDDDDD *
	 *fjt.       .;:::,,,,,,,;;;;EEKWWWWWWWWKWKKKKKKKKKKKKKKKWKKKKKKKKKKWKKWWWW#WW#KKKKKKii;;;;f;.............:tDEEEEEKKKKKKKKEti;;;L...............................EEKf;:iKKE::::::E::::::::::::::ifDDDDDDDDD *
	 *fjt:        :::,,,,,,,,;;;DEEWWWWWWWWWEKKKKKKKKKKKKKKKKKKKKKKKKKKWWKKWWWW####KKKKKEiii;;;;f,.........iDEEEEKKKKKKKKKKKKKKKf;iG......i..........................fK::::KKE::::::E::::::::::::::::,tGGDDDDD *
	 *fjt:       t:::,,,,,,;;;;iDEKWWWWWWKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWKKWWWW####WKKKKLiii;;;;;L,....,Li;EDEEEEKKKKKKKKKKKKKKKKiG......;:...........................:i:::KKE:::::,E,::::::::::::::::::iGDDDD *
	 *jjt.       f::,,,,,,,;;;;GEEWWWWKEEKEKKKKKKKKKKKKKKKKWKKKKKKKKKKKWWKWWWWW###WWKKKKiii;;;;;;;G,;L;;iiEEEEEEEKKKKKKKKKKKKKWWKE......;t.........:....................j::KEE:,::,,D,,::::,,,,,,:::::::::tDDD *
	 *fjt:.      ,::,,,,,,,;;;;EEWWKEEEEEEKKKKKKKKKKKKKKKKWKKKKKKKKKKKWWKKWWWWW#W#KKKKKKiiiiii;;;;;i;;iiiEEKEEKKWKKKKKKKWKKKKKWWWGi;...;t......,;;;;,....................:,EEE,,,,,,D,,,,,,,,,,,,,,,,::,::::tG *
	 *fjt:.     ,::,,,,,,,;;;;DEKEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWWWWWWWW#W#KKKKKKiiiii;;i;;;;;iiiKKKEKKKKWWKWWWWWWKKKKWWWWW;;;:;L.....;;;;;;;;;....................,KEE,,,,,,E,,,,,,,,,,,,,,,,,,,,,,,,; *
	 *fjt:.     f:,,,,,,,;;;;jEDEEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWWWWWWW#W##KKKKKKiiiiiiii;i;;iiiEKKKKKKKKWKWWWWWWWWKKKWWWWWKi;;i.....,jEEfGi;;;;;...................EED,,,,,,E,,,,,,,,,,,,,,,,,,,,,,,,, *
	 *fjt:.    .f::,,,,,,;;jEEDEEEEEEEEEEKKKKKKKKKKKKKKKWKKKKKKKKKKKKKWWWKWWWWW###KKKKKLiiiiiiiiiiiiiiEEKKKKKKKKWWWWWWWWWWWWKWWWWWWGi;i;,..;jDDDKEGi;;;;;;:................EED,,,,,,D,,,,,,,,,,,,,,,,,,,,,,,,, *
	 *fjt:.  .. ;::,,,,,;;EDDEEEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWKKW#WW####KWKKKiiiiiiiiiiiiijKKKKKKKKKKWWWWWWWWWWWWWWWWWWWWWt;i;;;;i;DDDDDDGi;;;;;;;;:.............EDf;,,,;,G;;;;;;;;;;;;;;;,,,,,,,,,, *
	 *fjt:......:,,,,,,;LDDDEEEEEEEEEEEKKKKKKKKKKKKKKKKWKKKKKKKKKKKKKWWWWKWWWW####KKKKKiiiiiiiiiiijKEKKWKKKKKKKWWWWWWWWWWWWWWWWWWWWWWiLiii;i;DEEEEDDE;i;;;;;;;;;:..........EDi,;;;;;L;;;;;;;;;;;;;;;;;;,,,,,,, *
	 *fjt:......:,,,,,;EDDDEEKEEEEEEEEEKKKKKKKKKKKKKKKWKKKKKKKKKKKKKKWWWWKKWWW##W#KWKKWEiiiiiijGKKKKKWWKKKKKKKKWWWWWWWWWWWWWWWWWWWWWWKi;iiiiDDEEEEEEDEi;;;;;;;;;;;;;,:.....ED;;;;;;;j;;;;;;;;;;;;;;;;;;;;;;;,, *
	 *fjt:.....t,,,,,;DDDDEEEKEEEEEEEEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWWKKKWWWW##WKWKKWKiiiKKKKKKKKKWWKKKKKKKKWWWWWWWWWWWWWWW#WWWWWWWWWiiiiifLEEEEEEEEDi;i;;;;;;;;;;;;.....DD;;;;;;;i;;;;;;;;;;;;;;;;;;;;;;;;; *
	 *fjt:.....G,,,,,GDDDEEEEEEEEEEEEKKKKKKKKKKKKKKKKWKKKKKKKKKKKKKKKWWWKKKWWW###WKWKKWKitKKKKKKKKKWKKKKKKKKKKWWWWWWWWWWWWWW###WWWWWWWWEiiiiiiiEEEEEEEEDGiiii;;;;;;;;;.....GD;;;;;;;i;;;;;;;;;;;;;;;;;;;;;;;;; *
	 *fjt:.....L,,,,;GDDDEEEEEEEEEEKEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKWWWWWDGWWW###KKWWKWKKKKKKKKKKKKKKKKKKKKKKKWWWWWWWWWWWWW####WWWWWWWWWiiiiiiiiEEEEEEEEEEDi;i;;;;;;;;.....Lj;;;;;;i;iiiiii;;;;;;ii;;;;;;;;;;; *
	 ***********************************************************************************************************************************************************************************************************/

	void sort(int a[]) {
		ArrayList<Integer> list=new ArrayList<>();
		for(int x: a) list.add(x);
		Collections.sort(list);
		for(int i=0;i<a.length;i++) a[i]=list.get(i);
	}
	void sort(long a[]) {
		ArrayList<Long> list=new ArrayList<>();
		for(long x: a) list.add(x);
		Collections.sort(list);
		for(int i=0;i<a.length;i++) a[i]=list.get(i);
	}
	void ruffleSort(int a[]) {
		Random rand=new Random();
		int n=a.length;
		for(int i=0;i<n;i++) {
			int j=rand.nextInt(n);
			int temp=a[i];
			a[i]=a[j];
			a[j]=temp;
		}
		Arrays.sort(a);
	}
	void ruffleSort(long a[]) {
		Random rand=new Random();
		int n=a.length;
		for(int i=0;i<n;i++) {
			int j=rand.nextInt(n);
			long temp=a[i];
			a[i]=a[j];
			a[j]=temp;
		}
		Arrays.sort(a);
	}
	
    static class FastReader { 
        BufferedReader br; 
        StringTokenizer st;
        public FastReader() { 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
        String next() { 
            while (st==null || !st.hasMoreElements()) { 
                try { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
        int nextInt() { 
            return Integer.parseInt(next()); 
        } 
        long nextLong() { 
            return Long.parseLong(next()); 
        } 
        double nextDouble() { 
            return Double.parseDouble(next()); 
        } 
        String nextLine() { 
            String s=""; 
            try { 
                s=br.readLine(); 
            } 
            catch (IOException e) { 
                e.printStackTrace(); 
            } 
            return s; 
        } 
    } 
    
	long fact[];
	long invFact[];
	void init(int n) {
		fact=new long[n+1];
		invFact=new long[n+1];
		fact[0]=1;
		for(int i=1;i<=n;i++) {
			fact[i]=mul(i,fact[i-1]);
		}
		invFact[n]=power(fact[n],mod-2);
		for(int i=n-1;i>=0;i--) {
			invFact[i]=mul(invFact[i+1],i+1);
		}
	}
	
	long nCr(int n, int r) {
		if(n<r || r<0) return 0;
		return mul(fact[n],mul(invFact[r],invFact[n-r]));
	}
	
	long mul(long a, long b) {
		return a*b%mod;
	}
	long add(long a, long b) {
		return (a+b)%mod;
	}
	
	long power(long x, long y) {
		long gg=1;
		while(y>0) {
			if(y%2==1) gg=mul(gg,x);
			x=mul(x,x);
			y/=2;
		}
		return gg;
	}
    
    // Functions
	static long gcd(long a, long b) { 
		return b==0?a:gcd(b,a%b);
	}
	static int gcd(int a, int b) { 
		return b==0?a:gcd(b,a%b);
	}
	
	void print(int a[]) {
		int n=a.length;
		for(int i=0;i<n;i++) out.print(a[i]+" ");
		out.println();
	}
	
	void print(long a[]) {
		int n=a.length;
		for(int i=0;i<n;i++) out.print(a[i]+" ");
		out.println();
	}
    
    //Input Arrays
    static void input(long a[], int n) {
		for(int i=0;i<n;i++) {
			a[i]=inp.nextLong();
		}
	}
	static void input(int a[], int n) {
		for(int i=0;i<n;i++) {
			a[i]=inp.nextInt();
		}
	}	
	static void input(String s[],int n) {
		for(int i=0;i<n;i++) {
			s[i]=inp.next();
		}
	}
	static void input(int a[][], int n, int m) {
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				a[i][j]=inp.nextInt();
			}
		}
	}
	static void input(long a[][], int n, int m) {
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				a[i][j]=inp.nextLong();
			}
		}
	}
		
}