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:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.Collection;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Random;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author aryssoncf
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        BGraphSubsetProblem solver = new BGraphSubsetProblem();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class BGraphSubsetProblem {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt(), m = in.readInt(), k = in.readInt();
            int[] u = new int[m], v = new int[m];
            in.readIntArrays(u, v);
            MiscUtils.decreaseByOne(u, v);
            EzIntSet[] graph = createGraph(n, m, u, v);
            solve(n, graph, k, out);
        }

        void solve(int n, EzIntSet[] graph, int k, OutputWriter out) {
            EzIntQueue queue = new EzIntArrayDeque();
            boolean[] used = new boolean[n];
            for (int i = 0; i < n; i++) {
                if (graph[i].size() < k) {
                    queue.add(i);
                    used[i] = true;
                }
            }
            while (!queue.isEmpty()) {
                int u = queue.removeFirst();
                if (graph[u].size() == k - 1 && checkClique(u, graph)) {
                    int[] res = new int[k];
                    res[0] = u;
                    System.arraycopy(graph[u].toArray(), 0, res, 1, k - 1);
                    MiscUtils.increaseByOne(res);
                    out.printLine(2);
                    out.printLine(res);
                    return;
                }
                for (EzIntIterator it = graph[u].iterator(); it.hasNext(); ) {
                    int v = it.next();
                    if (graph[v].size() == k) {
                        queue.add(v);
                        used[v] = true;
                    }
                    graph[v].remove(u);
                }
                graph[u].clear();
            }
            if (ArrayUtils.count(used, false) == 0) {
                out.printLine(-1);
            } else {
                int[] res = IntStream.range(0, n).filter(i -> !used[i]).toArray();
                MiscUtils.increaseByOne(res);
                out.printLine(1, res.length);
                out.printLine(res);
            }
        }

        boolean checkClique(int u, EzIntSet[] graph) {
            for (EzIntIterator it = graph[u].iterator(); it.hasNext(); ) {
                int v = it.next();
                for (EzIntIterator it2 = graph[u].iterator(); it2.hasNext(); ) {
                    int w = it2.next();
                    if (v != w && !graph[v].contains(w)) {
                        return false;
                    }
                }
            }
            return true;
        }

        EzIntSet[] createGraph(int n, int m, int[] u, int[] v) {
            EzIntSet[] res = new EzIntSet[n];
            Arrays.setAll(res, i -> new EzIntHashSet(0));
            for (int i = 0; i < m; i++) {
                res[u[i]].add(v[i]);
                res[v[i]].add(u[i]);
            }
            return res;
        }

    }

    static interface EzIntDeque extends EzIntQueue, EzIntStack {
        int size();

        boolean isEmpty();

        EzIntIterator iterator();

        boolean add(int element);

        boolean equals(Object object);

        int hashCode();

        String toString();

        int removeFirst();

    }

    static interface EzIntIterator {
        boolean hasNext();

        int next();

    }

    static class ArrayUtils {
        public static int count(boolean[] array, boolean value) {
            int result = 0;
            for (boolean i : array) {
                if (i == value) {
                    result++;
                }
            }
            return result;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void printLine(int[] array) {
            print(array);
            writer.println();
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void printLine(int i) {
            writer.println(i);
        }

    }

    static interface EzIntQueue extends EzIntCollection {
        int size();

        boolean isEmpty();

        EzIntIterator iterator();

        boolean add(int element);

        boolean equals(Object object);

        int hashCode();

        String toString();

        int removeFirst();

    }

    static interface EzIntList extends EzIntCollection {
        int size();

        EzIntIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static interface EzIntStack extends EzIntCollection {
        int size();

        EzIntIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static class MiscUtils {
        public static void decreaseByOne(int[] array) {
            for (int i = 0; i < array.length; i++) {
                array[i]--;
            }
        }

        public static void decreaseByOne(int[]... arrays) {
            for (int[] array : arrays) {
                decreaseByOne(array);
            }
        }

        public static void increaseByOne(int[] array) {
            for (int i = 0; i < array.length; i++) {
                array[i]++;
            }
        }

    }

    static final class EzIntSort {
        private static final double HEAPSORT_DEPTH_COEFFICIENT = 2.0;
        private static final Random rnd = new Random();

        private EzIntSort() {
        }

        private static int maxQuickSortDepth(int length) {
            if (length <= 1) {
                return 0;
            }
            int log = Integer.numberOfTrailingZeros(Integer.highestOneBit(length - 1)) + 1;
            return (int) (HEAPSORT_DEPTH_COEFFICIENT * log);
        }

        public static void sort(int[] a) {
            quickSort(a, 0, a.length, 0, maxQuickSortDepth(a.length));
        }

        private static void quickSort(int[] a, int left, int right, int depth, int maxDepth) {
            if (right - left <= 1) {
                return;
            }
            if (depth > maxDepth) {
                heapSort(a, left, right - left);
                return;
            }
            final int pivot = a[left + rnd.nextInt(right - left)];
            int i = left;
            int j = right - 1;
            do {
                while (a[i] < pivot) i++;
                while (pivot < a[j]) j--;
                if (i <= j) {
                    int tmp = a[i];
                    a[i++] = a[j];
                    a[j--] = tmp;
                }
            } while (i <= j);
            quickSort(a, left, j + 1, depth + 1, maxDepth);
            quickSort(a, i, right, depth + 1, maxDepth);
        }

        private static void heapSort(int[] a, int offset, int size) {
            // If size <= 1, nothing is executed
            for (int i = (size >>> 1) - 1; i >= 0; i--) {
                down(a, i, offset, size);
            }
            for (int i = size - 1; i > 0; i--) {
                int tmp = a[offset];
                a[offset] = a[offset + i];
                a[offset + i] = tmp;
                down(a, 0, offset, i);
            }
        }

        private static void down(int[] a, int index, int offset, int size) {
            final int element = a[offset + index];
            final int firstLeaf = (size >>> 1);
            while (index < firstLeaf) {
                int largestChild = (index << 1) + 1;
                if (largestChild + 1 < size && a[offset + largestChild + 1] > a[offset + largestChild]) {
                    largestChild++;
                }
                if (a[offset + largestChild] <= element) {
                    break;
                }
                a[offset + index] = a[offset + largestChild];
                index = largestChild;
            }
            a[offset + index] = element;
        }

    }

    static interface EzIntCollection {
        int size();

        EzIntIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static class EzIntArrayDeque implements EzIntDeque, EzIntList {
        private static final int DEFAULT_CAPACITY = 8;
        private static final int HASHCODE_INITIAL_VALUE = 0x811c9dc5;
        private static final int HASHCODE_MULTIPLIER = 0x01000193;
        private int[] deque;
        private int size;
        private int head;
        private int tail;
        private int mask;

        public EzIntArrayDeque() {
            this(DEFAULT_CAPACITY);
        }

        public EzIntArrayDeque(int capacity) {
            if (capacity < 0) {
                throw new IllegalArgumentException("Capacity must be non-negative");
            }
            if (capacity < 1) {
                capacity = 1;
            }
            if ((capacity & (capacity - 1)) != 0) {
                capacity = Integer.highestOneBit(capacity) << 1;
            }
            // Capacity is a power of 2 now
            deque = new int[capacity];
            size = 0;
            head = 0;
            tail = 0;
            mask = deque.length - 1;
        }

        public EzIntArrayDeque(EzIntCollection collection) {
            this(collection.size() + 1);
            for (EzIntIterator iterator = collection.iterator(); iterator.hasNext(); ) {
                deque[tail++] = iterator.next();
            }
            size = collection.size();
        }

        public EzIntArrayDeque(int[] srcArray) {
            this(srcArray.length + 1);
            System.arraycopy(srcArray, 0, deque, 0, srcArray.length);
            tail = srcArray.length;
            size = srcArray.length;
        }

        public EzIntArrayDeque(Collection<Integer> javaCollection) {
            this(javaCollection.size() + 1);
            for (int element : javaCollection) {
                deque[tail++] = element;
            }
            size = javaCollection.size();
        }

        public int size() {
            return size;
        }

        public boolean isEmpty() {
            return size == 0;
        }

        public EzIntIterator iterator() {
            return new EzIntArrayDequeIterator();
        }

        public boolean add(int element) {
            deque[tail] = element;
            tail = (tail + 1) & mask;
            size++;
            if (size == deque.length) {
                enlarge();
            }
            return true;
        }

        public int removeFirst() {
            if (size == 0) {
                throw new NoSuchElementException("Trying to call removeFirst() on empty ArrayDeque");
            }
            final int removedElement = deque[head];
            size--;
            head = (head + 1) & mask;
            return removedElement;
        }

        private void enlarge() {
            int newSize = (size << 1);
            int[] newArray = new int[newSize];
            System.arraycopy(deque, head, newArray, 0, deque.length - head);
            System.arraycopy(deque, 0, newArray, deque.length - tail, tail);
            deque = newArray;
            head = 0;
            tail = size;
            mask = deque.length - 1;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            EzIntArrayDeque that = (EzIntArrayDeque) o;

            if (size != that.size) {
                return false;
            }
            for (int i = head, j = that.head; i != tail; i = (i + 1) & mask, j = (j + 1) & that.mask) {
                if (deque[i] != that.deque[j]) {
                    return false;
                }
            }
            return true;
        }

        public int hashCode() {
            int hash = HASHCODE_INITIAL_VALUE;
            for (int i = head; i != tail; i = (i + 1) & mask) {
                hash = (hash ^ PrimitiveHashCalculator.getHash(deque[i])) * HASHCODE_MULTIPLIER;
            }
            return hash;
        }

        public String toString() {
            StringBuilder sb = new StringBuilder();
            sb.append('[');
            for (int i = head; i != tail; i = (i + 1) & mask) {
                if (i != head) {
                    sb.append(", ");
                }
                sb.append(deque[i]);
            }
            sb.append(']');
            return sb.toString();
        }

        private class EzIntArrayDequeIterator implements EzIntIterator {
            private int curIndex = head;

            public boolean hasNext() {
                return curIndex != tail;
            }

            public int next() {
                if (curIndex == tail) {
                    throw new NoSuchElementException("Iterator doesn't have more elements");
                }
                final int result = deque[curIndex];
                curIndex = (curIndex + 1) & mask;
                return result;
            }

        }

    }

    static final class PrimitiveHashCalculator {
        private PrimitiveHashCalculator() {
        }

        public static int getHash(int x) {
            return x;
        }

    }

    static class EzIntHashSet implements EzIntSet {
        private static final int DEFAULT_CAPACITY = 8;
        private static final int REBUILD_LENGTH_THRESHOLD = 32;
        private static final int HASHCODE_INITIAL_VALUE = 0x811c9dc5;
        private static final int HASHCODE_MULTIPLIER = 0x01000193;
        private static final byte FREE = 0;
        private static final byte REMOVED = 1;
        private static final byte FILLED = 2;
        private static final Random rnd = new Random();
        private static final int POS_RANDOM_SHIFT_1;
        private static final int POS_RANDOM_SHIFT_2;
        private static final int STEP_RANDOM_SHIFT_1;
        private static final int STEP_RANDOM_SHIFT_2;
        private int[] table;
        private byte[] status;
        private int size;
        private int removedCount;
        private int mask;
        private final int hashSeed;

        static {
            POS_RANDOM_SHIFT_1 = rnd.nextInt(10) + 11;
            POS_RANDOM_SHIFT_2 = rnd.nextInt(10) + 21;
            STEP_RANDOM_SHIFT_1 = rnd.nextInt(10) + 11;
            STEP_RANDOM_SHIFT_2 = rnd.nextInt(10) + 21;
        }

        public EzIntHashSet() {
            this(DEFAULT_CAPACITY);
        }

        public EzIntHashSet(int capacity) {
            if (capacity < 0) {
                throw new IllegalArgumentException("Capacity must be non-negative");
            }
            // Actually we need 4x more memory
            int length = 4 * Math.max(1, capacity);
            if ((length & (length - 1)) != 0) {
                length = Integer.highestOneBit(length) << 1;
            }
            // Length is a power of 2 now
            initEmptyTable(length);
            hashSeed = rnd.nextInt();
        }

        public EzIntHashSet(EzIntCollection collection) {
            this(collection.size());
            for (EzIntIterator iterator = collection.iterator(); iterator.hasNext(); ) {
                add(iterator.next());
            }
        }

        public EzIntHashSet(int[] srcArray) {
            this(srcArray.length);
            for (int element : srcArray) {
                add(element);
            }
        }

        public EzIntHashSet(Collection<Integer> javaCollection) {
            this(javaCollection.size());
            for (int element : javaCollection) {
                add(element);
            }
        }

        private int getStartPos(int h) {
            h ^= hashSeed;
            h ^= (h >>> POS_RANDOM_SHIFT_1) ^ (h >>> POS_RANDOM_SHIFT_2);
            return h & mask;
        }

        private int getStep(int h) {
            h ^= hashSeed;
            h ^= (h >>> STEP_RANDOM_SHIFT_1) ^ (h >>> STEP_RANDOM_SHIFT_2);
            return ((h << 1) | 1) & mask;
        }

        public int size() {
            return size;
        }

        public boolean contains(int element) {
            final int elementHash = PrimitiveHashCalculator.getHash(element);
            int pos = getStartPos(elementHash);
            final int step = getStep(elementHash);
            for (; status[pos] != FREE; pos = (pos + step) & mask) {
                if (status[pos] == FILLED && table[pos] == element) {
                    return true;
                }
            }
            return false;
        }

        public EzIntIterator iterator() {
            return new EzIntHashSetIterator();
        }

        public int[] toArray() {
            int[] result = new int[size];
            for (int i = 0, j = 0; i < table.length; i++) {
                if (status[i] == FILLED) {
                    result[j++] = table[i];
                }
            }
            return result;
        }

        public boolean add(int element) {
            final int elementHash = PrimitiveHashCalculator.getHash(element);
            int pos = getStartPos(elementHash);
            final int step = getStep(elementHash);
            for (; status[pos] == FILLED; pos = (pos + step) & mask) {
                if (table[pos] == element) {
                    return false;
                }
            }
            if (status[pos] == FREE) {
                status[pos] = FILLED;
                table[pos] = element;
                size++;
                if ((size + removedCount) * 2 > table.length) {
                    rebuild(table.length * 2); // enlarge the table
                }
                return true;
            }
            final int removedPos = pos;
            for (pos = (pos + step) & mask; status[pos] != FREE; pos = (pos + step) & mask) {
                if (status[pos] == FILLED && table[pos] == element) {
                    return false;
                }
            }
            status[removedPos] = FILLED;
            table[removedPos] = element;
            size++;
            removedCount--;
            return true;
        }

        public boolean remove(int element) {
            final int elementHash = PrimitiveHashCalculator.getHash(element);
            int pos = getStartPos(elementHash);
            final int step = getStep(elementHash);
            for (; status[pos] != FREE; pos = (pos + step) & mask) {
                if (status[pos] == FILLED && table[pos] == element) {
                    status[pos] = REMOVED;
                    size--;
                    removedCount++;
                    if (table.length > REBUILD_LENGTH_THRESHOLD) {
                        if (8 * size <= table.length) {
                            rebuild(table.length / 2); // compress the table
                        } else if (size < removedCount) {
                            rebuild(table.length); // just rebuild the table
                        }
                    }
                    return true;
                }
            }
            return false;
        }

        public void clear() {
            if (table.length > REBUILD_LENGTH_THRESHOLD) {
                initEmptyTable(REBUILD_LENGTH_THRESHOLD);
            } else {
                Arrays.fill(status, FREE);
                size = 0;
                removedCount = 0;
            }
        }

        private void rebuild(int newLength) {
            int[] oldTable = table;
            byte[] oldStatus = status;
            initEmptyTable(newLength);
            for (int i = 0; i < oldTable.length; i++) {
                if (oldStatus[i] == FILLED) {
                    add(oldTable[i]);
                }
            }
        }

        private void initEmptyTable(int length) {
            table = new int[length];
            status = new byte[length];
            size = 0;
            removedCount = 0;
            mask = length - 1;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            EzIntHashSet that = (EzIntHashSet) o;

            if (size != that.size) {
                return false;
            }
            for (int i = 0; i < table.length; i++) {
                if (status[i] == FILLED) {
                    if (!that.contains(table[i])) {
                        return false;
                    }
                }
            }
            return true;
        }

        public int hashCode() {
            int[] array = toArray();
            EzIntSort.sort(array);
            int hash = HASHCODE_INITIAL_VALUE;
            for (int i = 0; i < size; i++) {
                hash = (hash ^ PrimitiveHashCalculator.getHash(array[i])) * HASHCODE_MULTIPLIER;
            }
            return hash;
        }

        public String toString() {
            StringBuilder sb = new StringBuilder();
            sb.append('[');
            for (int i = 0; i < table.length; i++) {
                if (status[i] == FILLED) {
                    if (sb.length() > 1) {
                        sb.append(", ");
                    }
                    sb.append(table[i]);
                }
            }
            sb.append(']');
            return sb.toString();
        }

        private class EzIntHashSetIterator implements EzIntIterator {
            private int curIndex = 0;

            public boolean hasNext() {
                while (curIndex < table.length && status[curIndex] != FILLED) {
                    curIndex++;
                }
                return curIndex < table.length;
            }

            public int next() {
                while (curIndex < table.length && status[curIndex] != FILLED) {
                    curIndex++;
                }
                if (curIndex == table.length) {
                    throw new NoSuchElementException("Iterator doesn't have more elements");
                }
                return table[curIndex++];
            }

        }

    }

    static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public void readIntArrays(int[]... arrays) {
            int length = (int) Arrays.stream(arrays[0]).count();
            for (int i = 0; i < length; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = readInt();
                }
            }
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);

        }

    }

    static interface EzIntSet extends EzIntCollection {
        int size();

        boolean contains(int element);

        EzIntIterator iterator();

        int[] toArray();

        boolean add(int element);

        boolean remove(int element);

        void clear();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }
}