Problem: This problem is interactive.

We have hidden a permutation p_1, p_2, ..., p_n of numbers from 1 to n from you, where n is even. You can try to guess it using the following queries:

? k a_1 a_2 ... a_k.

In response, you will learn if the average of elements with indexes a_1, a_2, ..., a_k is an integer. In other words, you will receive 1 if \frac{p_{a_1} + p_{a_2} + ... + p_{a_k}}{k} is integer, and 0 otherwise. 

You have to guess the permutation. You can ask not more than 18n queries.

Note that permutations [p_1, p_2, ..., p_k] and [n + 1 - p_1, n + 1 - p_2, ..., n + 1 - p_k] are indistinguishable. Therefore, you are guaranteed that p_1 ≤ n/2.

Note that the permutation p is fixed before the start of the interaction and doesn't depend on your queries. In other words, interactor is not adaptive.

Note that you don't have to minimize the number of queries.

Input

The first line contains a single integer n (2 ≤ n ≤ 800, n is even).

Interaction

You begin the interaction by reading n.

To ask a question about elements on positions a_1, a_2, ..., a_k, in a separate line output

? k a_1 a_2 ... a_k

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

In response, you will receive 1 if \frac{p_{a_1} + p_{a_2} + ... + p_{a_k}}{k} is integer, and 0 otherwise. 

In case your query is invalid or you asked more than 18n 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 permutation, output 

! p_1 p_2 ... p_n

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 a single integer n (2 ≤ n ≤ 800, n is even).

In the next line output n integers p_1, p_2, ..., p_n — the valid permutation of numbers from 1 to n. p_1 ≤ n/2 must hold.

Example

Input


2
1 2


Output


? 1 2
? 1 1
! 1 2 

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;

// written by luchy0120

public class Main {
    public static void main(String[] args) throws Exception {

        new Main().run();
    }

    static int groups = 0;
    static int[] fa;
    static int[] sz;

    static void init(int n) {
        groups = n;
        fa = new int[n];
        for (int i = 1; i < n; ++i) {
            fa[i] = i;
        }
        sz = new int[n];
        Arrays.fill(sz, 1);
    }

    static int root(int p) {
        while (p != fa[p]) {
            fa[p] = fa[fa[p]];
            p = fa[p];
        }
        return p;
    }

    static void combine(int p, int q) {
        int i = root(p);
        int j = root(q);
        if (i == j) {
            return;
        }
        if (sz[i] < sz[j]) {
            fa[i] = j;
            sz[j] += sz[i];
        } else {
            fa[j] = i;
            sz[i] += sz[j];
        }
        groups--;
    }


    int color[],dfn[],low[],stack[],cnt[];
    boolean vis[];
    boolean iscut[];
    int deep,top,n,m,sum,ans;
    List<Integer> g[];

    void tarjan(int u,int fa) {
        int child = 0;
        dfn[u]=++deep;
        low[u]=deep;
        vis[u]=true;
        stack[++top]=u;
        int sz=g[u].size();
        for(int i=0;i<sz;i++) {
            int v =g[u].get(i);
            if(v==fa) continue;
            if(dfn[v]==0) {
                child++;
                tarjan(v,u);
                low[u]=Math.min(low[u],low[v]);
            } else {
                if(vis[v]) {
                    low[u]=Math.min(low[u],low[v]);
                }
            }
        }
        if(fa<0&&child==1){
            iscut[u] =true;
        }

        if(dfn[u]==low[u]) {
            iscut[u] = true;
            color[u]=++sum;
            vis[u]=false;
            while(stack[top]!=u) {
                color[stack[top]]=sum;
                vis[stack[top--]]=false;
            }
            top--;
        }
    }


    int h[],to[],ne[];int ct =0;
    void add(int u,int v){
        u--;v--;
        to[ct] = v;
        ne[ct] = h[u];
        h[u] = ct++;
    }

    void graph(int n,int m){
        h = new int[n];
        Arrays.fill(h,-1);
        ne = new int[2*m];
        to = new int[2*m];
        ct = 0;
    }


    static long mul(long a, long b, long p)
    {
        long res=0,base=a;
        while(b>0)
        {
            if((b&1L)>0)
                res=(res+base)%p;
            base=(base+base)%p;
            b>>=1;
        }
        return res;
    }


    static long mod_pow(long k,long n,long p){
        long res = 1L;
        long temp = (k%p+p)%p;
        while(n!=0L){
            if((n&1L)==1L){
                res = ((res*temp)%p+p)%p;
            }
            temp = ((temp * temp)%p+p)%p;
            n = n>>1L;
        }
        return res%p;
    }
    public static String roundS(double result, int scale){
        String fmt = String.format("%%.%df", scale);
        return String.format(fmt, result);
    }

    int x[];
    int y[];
    int k ;
    int r = 1000000000;
    int[][] pos;

    boolean gd(int i){
        if(pos[i][0]<pos[i][1]) return false;
        if(pos[i][2]>pos[i][3]) return false;
        return true;
    }


    int area(int i){
        if(pos[i][0]<=pos[i][1]) return 0;
        if(pos[i][2]>=pos[i][3]) return 0;
        return (pos[i][0]-pos[i][1])*(pos[i][3]-pos[i][2]);
    }

    boolean in(int i,int y,int x){
        return y<=pos[i][0]&&y>=pos[i][1] && x<=pos[i][3] && x>= pos[i][2];
    }


    boolean ck(int i,int j){
        return !in(i, pos[j][0],pos[j][3]) &&
        !in(i, pos[j][0],pos[j][2]) &&
        !in(i, pos[j][1],pos[j][2]) &&
        !in(i, pos[j][1],pos[j][3]);
    }

    void go(int c,int sum){
        if(sum>=r) return;
        if(c==n){
            for(int i=0;i<k;++i) {
                if (!gd(i)) return;
            }

            for(int i=0;i<k;++i){
                for(int j=i+1;j<k;++j){
                    if(!ck(i,j)){
                        return;
                    }
                }
            }
            r = sum;
            return;
        }

        for(int i=0;i<k;++i){
            int tmp[] = pos[i].clone();
            int zx = x[c];
            int zy = y[c];

            int prev = area(i);

            pos[i][0] = Math.max(pos[i][0],zy);
            pos[i][1] = Math.min(pos[i][1],zy);

            pos[i][2] = Math.min(pos[i][2],zx);
            pos[i][3] = Math.max(pos[i][3],zx);

            int cur = area(i);

            go(c+1,sum-prev+cur);

            pos[i] = tmp;
        }

    }


    int dx[] = {0,0,1,-1};
    int dy[] = {1,-1,0,0};
    boolean xiao(int mp[][]){
        boolean ok = false;
        boolean mk[][] = new boolean[7][5];
        for(int i=0;i<7;++i){
            for(int j=0;j<5;++j){
                if(mp[i][j]==0) continue;
                int k = j+1;
                int c = mp[i][j];
                while(k<5&&mp[i][k]==c) k++;
                if(k-j>=3){
                    ok = true;
                    for(int u=j;u<k;++u){
                        mk[i][u] = true;
                    }
                }
            }
        }

        for(int i=0;i<5;++i){
            for(int j=6;j>=0;--j){
                if(mp[i][j]==0) break;
                int k = j-1;
                int c = mp[i][j];
                while(k>=0&&mp[i][k]==c) k--;
                if(j-k>=3){
                    ok = true;
                    for(int u=j;u>k;--u){
                        mk[i][u] = true;
                    }
                }
            }
        }

        for(int i=0;i<7;++i) {
            for (int j = 0; j < 5; ++j) {
                if (mp[i][j] > 0 && mk[i][j]) {
                    mp[i][j] = 0;
                }
            }
        }
      return ok;
    }

    void luo(int[][] mp){
        for(int i=0;i<5;++i){
            int f = 6;
            for(int j=6;j>=0;--j){
                if(mp[i][j]==0) continue;
                mp[i][f] = mp[i][j];f--;
                mp[i][j] = 0;
            }
        }
    }


    void go(int mp[][]){



        while(xiao(mp)){
            luo(mp);
        }



    }

    void sort(int a[]){
        Arrays.sort(a);
    }


    int gcd(int a,int b){
        return b==0?a:gcd(b,a%b);
    }

    void solve() {
//        int n = ni();
//        int mp[][] = new int[7][5];
//        // less than 10;
//
//        for(int i=0;i<5;++i){
//            int x = 6;
//            while(true){
//                int num = ni();
//                if(num==0) break;
//                mp[x][i] = num;
//                x--;
//            }
//        }
            int n = ni();
            int k = ni();
            int pos1 = -1;
            int pos2 = -1;
            StringBuilder sb = new StringBuilder();
            sb.append("? ");
            for(int i=1;i<=k;++i){
                sb.append(i);
                if(i!=k){
                    sb.append(" ");
                }
            }
            println(sb);out.flush();
            pos1 = ni();
            int a[] = new int[k+2];
            a[pos1] = ni();

        sb = new StringBuilder();
        sb.append("? ");
        for(int i=1;i<=k;++i){
            if(i==pos1) continue;
            sb.append(i);
            sb.append(" ");
        }
        sb.append(k+1);
        println(sb);out.flush();
        pos2 = ni();
        a[pos2] = ni();
        int same = 0;
        for(int skip=1;skip<=k+1;++skip) {
            if (skip == pos1 || skip == pos2) continue;
            sb = new StringBuilder();
            sb.append("? ");
            for (int i = 1; i <= k + 1; ++i) {
                if (i == pos1 || i == pos2 || i == skip) continue;
                sb.append(i);
                sb.append(" ");
            }
            sb.append(pos1+" ");
            sb.append(pos2);
            println(sb); out.flush();
            ni();
            int v =ni();
            if(v==a[pos2]){
                same++;
            }
        }

        if(a[pos1]<a[pos2]){
            println("! "+(same+1));out.flush();
        }else{
            println("! "+(k-same));out.flush();
        }
















    }





    InputStream is;
    PrintWriter out;

    void run() throws Exception {
        is = System.in;
        out = new PrintWriter(System.out);
        solve();
        out.flush();
    }

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private double nd() {
        return Double.parseDouble(ns());
    }

    private char nc() {
        return (char) skip();
    }

    private char ncc() {
        int b = readByte();
        return (char) b;
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private String nline() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!isSpaceChar(b) || b == ' ') {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[][] nm(int n, int m) {
        char[][] a = new char[n][];
        for (int i = 0; i < n; i++) a[i] = ns(m);
        return a;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private long[] nal(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = nl();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
        }
        ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') num = (num << 3) + (num << 1) + (b - '0');
            else return minus ? -num : num;
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
        }
        ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') num = num * 10 + (b - '0');
            else return minus ? -num : num;
            b = readByte();
        }
    }

    void print(Object obj) {
        out.print(obj);
    }

    void println(Object obj) {
        out.println(obj);
    }

    void println() {
        out.println();
    }

    void printArray(int a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }

    void printArray(long a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }
}