Problem: This problem is interactive.

We have hidden an array a of n pairwise different numbers (this means that no two numbers are equal). You can get some information about this array using a new device you just ordered on Amazon. 

This device can answer queries of the following form: in response to the positions of k different elements of the array, it will return the position and value of the m-th among them in the ascending order.

Unfortunately, the instruction for the device was lost during delivery. However, you remember k, but don't remember m. Your task is to find m using queries to this device. 

You can ask not more than n queries.

Note that the array a and number m are fixed before the start of the interaction and don't depend on your queries. In other words, interactor is not adaptive.

Note that you don't have to minimize the number of queries, and you don't need to guess array a. You just have to guess m.

Input

The first line contains two integers n and k (1≤ k < n ≤ 500) — the length of the array and the number of the elements in the query.

It is guaranteed that number m satisfies 1≤ m ≤ k, elements a_1, a_2, ..., a_n of the array satisfy 0≤ a_i ≤ 10^9, and all of them are different.

Interaction

You begin the interaction by reading n and k.

To ask a question about elements on positions x_1, x_2, ..., x_k, in a separate line output

? x_1 x_2 x_3 ... x_k

Numbers in the query have to satisfy 1 ≤ x_i ≤ n, and all x_i have to be different. Don't forget to 'flush', to get the answer.

In response, you will receive two integers pos and a_{pos} — the position in the array a of the m-th in ascending order element among a_{x_1}, a_{x_2}, ..., a_{x_k}, and the element on this position.

In case your query is invalid or you asked more than n queries, the program will print -1 and will finish interaction. You will receive a Wrong answer verdict. Make sure to exit immediately to avoid getting other verdicts.

When you determine m, output 

! m

After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see documentation for other languages.



Hack format

For the hacks use the following format:

The first line has to contain three integers n, k, m (1 ≤ m ≤ k < n ≤ 500) — the length of the array, number of elements in the query, and which in the ascending order number the device returns.

In the next line output n integers a_1, a_2, ..., a_n (0≤ a_i ≤ 10^9) — the elements of the array. They have to be pairwise different.

Example

Input


4 3
4 9
4 9
4 9
1 2

Output


? 2 3 4
? 1 3 4
? 1 2 4
? 1 2 3
! 3

Note

In the example, n = 4, k = 3, m = 3, a = [2, 0, 1, 9].

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class SolutionD {

    private static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

    public static void main(String[] args) throws IOException {
        Reader reader = new Reader();
        int[] nk = reader.readIntNumbers();
        int k = nk[1];
        Map<Integer, Integer> valueToPos = new HashMap<>();
        Map<String, Integer> queryToValue = new HashMap<>();
        Map<Integer, Integer> discardedIndexToValue = new HashMap<>();
        for (int i = 1; i <= k + 1; i++) {
            String query = createQuery(k + 1, i);
            bw.write(query);
            bw.newLine();
            bw.flush();
            int[] posAndValue = reader.readIntNumbers();
            int pos = posAndValue[0];
            int value = posAndValue[1];
            valueToPos.put(value, pos);
            queryToValue.put(query, value);
            discardedIndexToValue.put(i, value);
        }


        String answer = "! " + getAnswer(discardedIndexToValue, valueToPos, k);
        bw.write(answer);
        bw.newLine();
        bw.flush();
    }

    private static String createQuery(int k, Integer valueToSkip) {
        String query = IntStream.rangeClosed(1, k)
                .filter(i -> i != valueToSkip)
                .mapToObj(String::valueOf)
                .collect(Collectors.joining(" ", "? ", ""));
        return query;
    }

    private static int getAnswer(Map<Integer, Integer> discardedIndexToValue, Map<Integer, Integer> valueToPos, int k) {
        Map<Integer, Set<Integer>> graph = new HashMap<>();
        for (int i = 1; i <= k + 1; i++) {
            graph.put(i, new HashSet<>());
        }

        List<Integer> discardedIndexes = new ArrayList<>(discardedIndexToValue.keySet());
        for (int i = 0; i < discardedIndexes.size(); i++) {
            for (int j = i + 1; j < discardedIndexes.size(); j++) {

                int value1 = discardedIndexToValue.get(discardedIndexes.get(i));
                int value2 = discardedIndexToValue.get(discardedIndexes.get(j));
                int pos1 = valueToPos.get(value1);
                int pos2 = valueToPos.get(value2);

                int index1 = discardedIndexes.get(j);
                int index2 = discardedIndexes.get(i);


                if (pos1 == pos2) {// it means that index1 and index2 stand on the same side from pos

                }

                if (index1 != pos1 && index2 != pos2) {
                    if (value1 < value2) { // it means that index1 < pos1 < index2 and index1 < pos2 < index2
                        graph.get(index1).add(pos1);
                        graph.get(index1).add(pos2);

                        graph.get(pos1).add(index2);
                        graph.get(pos2).add(index2);
                    } else if (value1 > value2) { // it means that index1 > pos1 > index2 and index1 > pos2 > index2
                        graph.get(index2).add(pos1);
                        graph.get(index2).add(pos2);

                        graph.get(pos1).add(index1);
                        graph.get(pos2).add(index1);
                    }

                }

                if (index1 != pos1 && index2 == pos2) {
                    if (value1 < value2) { // it means that index1 < pos1 < index2(pos2) and index2 is right after pos1
                        graph.get(index1).add(pos1);
                        graph.get(pos1).add(index2);
                    } else if (value1 > value2) { // it means that index1 > pos1 > index2(pos2) and index2 is right before pos1
                        graph.get(index2).add(pos1);
                        graph.get(pos1).add(index1);
                    }
                }

                if (index1 == pos1 && index2 != pos2) {
                    if (value1 < value2) {
                        graph.get(index1).add(pos2);
                        graph.get(pos2).add(index2);
                    } else if (value1 > value2) {
                        graph.get(index2).add(pos2);
                        graph.get(pos2).add(index1);
                    }
                }

                if (index1 == pos1 && index2 == pos2) {
                    if (value1 < value2) {
                        graph.get(index1).add(index2);
                    } else if (value1 > value2) {
                        graph.get(index2).add(index1);
                    }
                }

            }
        }

        return getResultFromGraphAndQueries(graph, k, discardedIndexes.get(0), valueToPos.get(discardedIndexToValue.get(discardedIndexes.get(0))));
    }

    private static int getResultFromGraphAndQueries(Map<Integer, Set<Integer>> graph, int k, Integer discardedIndex, int queryResultPos) {
        Set<Integer> parsedQuery = parseQueryToIntegerSet(createQuery(k + 1, discardedIndex));
        List<Integer> topologicallySorted = sortGraphTopologically(graph);
        int answer = -1;
        int index = 0;
        for(int v : topologicallySorted) {
            if(parsedQuery.contains(v)) {
                index++;
                if(v == queryResultPos) {
                    answer = index;
                    break;
                }
            }
        }

        return answer;
    }

    private static List<Integer> sortGraphTopologically(Map<Integer, Set<Integer>> graph) {
        Deque<Integer> sortedVertexes = new LinkedList<>();
        Set<Integer> usedInSortingVertexes = new HashSet<>();
        Set<Integer> usedVertexes = new HashSet<>();
        Deque<Integer> dfsStack = new LinkedList<>();

        List<Integer> vertexes = new ArrayList<>(graph.keySet());
        for (int i = 0; i < vertexes.size(); i++) {
            Integer startVertex = vertexes.get(i);
            if(usedVertexes.contains(startVertex)) {
                continue;
            }
            dfsStack.push(startVertex);
            while (!dfsStack.isEmpty()) {
                Integer vertex = dfsStack.getFirst();
                if(usedVertexes.contains(vertex)) {
                    dfsStack.pop();
                    if(!usedInSortingVertexes.contains(vertex)) {
                        sortedVertexes.push(vertex);
                        usedInSortingVertexes.add(vertex);
                    }
                } else {
                    usedVertexes.add(vertex);
                    Set<Integer> adjacentVertexes = graph.get(vertex);
                    if (adjacentVertexes != null && !adjacentVertexes.isEmpty()) {
                        adjacentVertexes.stream().filter(v -> !usedVertexes.contains(v)).forEach(dfsStack::push);
                    }
                }
            }
        }

        List<Integer> topologicalSorting = new ArrayList<>();
        IntStream.range(0, sortedVertexes.size()).forEachOrdered(i -> topologicalSorting.add(sortedVertexes.removeFirst()));
        return topologicalSorting;
    }

    private static int[] getQueriesDifference(Set<Integer> intQuery1, Set<Integer> intQuery2) {
        int[] res = new int[2];
        for (Integer inFirst : intQuery1) {
            if (!intQuery2.contains(inFirst)) {
                res[0] = inFirst;
                break;
            }
        }
        for (Integer inSecond : intQuery2) {
            if (!intQuery1.contains(inSecond)) {
                res[1] = inSecond;
                break;
            }
        }
        return res;
    }

    private static Set<Integer> parseQueryToIntegerSet(String query) {
        query = query.substring(2);
        return Arrays.stream(query.split(" ")).map(Integer::valueOf).collect(Collectors.toSet());
    }

}

class Reader {

    BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));

    public StringTokenizer getStringTokenizer() throws IOException {
        String line = bufferedReader.readLine().replaceAll("\\s+$", "");
        return new StringTokenizer(line, " ");
    }

    public int getNextInt(StringTokenizer stringTokenizer) {
        while (stringTokenizer.hasMoreTokens()) {
            return Integer.parseInt(stringTokenizer.nextToken());
        }
        throw new RuntimeException("no more tokens in string");
    }

    public long getNextLong(StringTokenizer stringTokenizer) {
        while (stringTokenizer.hasMoreTokens()) {
            return Long.parseLong(stringTokenizer.nextToken());
        }
        throw new RuntimeException("no more tokens in string");
    }

    public String getNextString(StringTokenizer stringTokenizer) {
        while (stringTokenizer.hasMoreTokens()) {
            return stringTokenizer.nextToken();
        }
        throw new RuntimeException("no more tokens in string");
    }


    public String readStringValue() throws IOException {
        return bufferedReader.readLine().replaceAll("\\s+$", "");
    }

    public int readIntValue() throws IOException {
        String line = bufferedReader.readLine().replaceAll("\\s+$", "");
        int parsedToInt = Integer.parseInt(line);
        return parsedToInt;
    }

    public int[] readIntNumbers() throws IOException {
        String[] line = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");
        int[] parsedToInt = Arrays.stream(line).mapToInt(Integer::parseInt).toArray();
        return parsedToInt;
    }

    public long readLongValue() throws IOException {
        String line = bufferedReader.readLine().replaceAll("\\s+$", "");
        long parsedToLong = Long.parseLong(line);
        return parsedToLong;
    }

    public long[] readLongNumbers() throws IOException {
        String[] line = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");
        long[] parsedToLong = Arrays.stream(line).mapToLong(Long::parseLong).toArray();
        return parsedToLong;
    }


}