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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.stream.IntStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.stream.Collectors;
import java.io.UncheckedIOException;
import java.util.List;
import java.util.stream.Stream;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        DStrangeDevice solver = new DStrangeDevice();
        solver.solve(1, in, out);
        out.close();
    }

    static class DStrangeDevice {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            DStrangeDevice.Interactor intr = new DStrangeDevice.Interactor(in, out);
            //Interactor intr = new FakeInteractor(in, out, 5, 1, 2, 0, 1, 9, 3, 8, 7, 5, 4);
            int n = intr.n, k = intr.k;

            int[] query = IntStream.range(0, k).toArray();
            DStrangeDevice.Answer first = intr.query(query);
            query[first.index] = k;
            DStrangeDevice.Answer second = intr.query(query);

            if (first.value > second.value) {
                DStrangeDevice.Answer t = first;
                first = second;
                second = t;
            }

            int ans = 0;
            for (int i = 0; i <= k; i++) {
                if (i == first.index || i == second.index) continue;

                int cur = 0;
                for (int j = 0; j <= k; j++) {
                    if (i == j) continue;
                    query[cur++] = j;
                }
                if (intr.query(query).index != first.index) ans++;
            }
            intr.answer(ans + 1);
        }

        private static class Interactor {
            private final int n;
            private final int k;
            private final LightScanner in;
            private final LightWriter out;
            private final List<Integer> nat;
            private final List<Integer> rev;

            public Interactor(LightScanner in, LightWriter out, int n, int k) {
                this.n = n;
                this.k = k;
                this.in = in;
                this.out = out;
                nat = IntStream.range(0, n).boxed().collect(Collectors.toList());
                Collections.shuffle(nat);
                rev = Arrays.asList(new Integer[n]);
                for (int i = 0; i < n; i++) rev.set(nat.get(i), i);
            }

            public Interactor(LightScanner in, LightWriter out) {
                this(in, out, in.ints(), in.ints());
            }

            DStrangeDevice.Answer query(int... q) {
                out.ans('?');
                for (int x : q) out.ans(nat.get(x) + 1);
                out.ln().flush();
                return new DStrangeDevice.Answer(rev.get(in.ints() - 1), in.ints());
            }

            void answer(int m) {
                out.ans('!').ans(m).ln().flush();
            }

        }

        private static class Answer {
            int index;
            int value;

            public Answer(int index, int value) {
                this.index = index;
                this.value = value;
            }

        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(char c) {
            if (!breaked) {
                print(' ');
            }
            return print(c);
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public LightWriter flush() {
            try {
                out.flush();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

    }
}