Codeforces 1270D 思维题

D. Strange Device

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

This problem is interactive.

We have hidden an array aa of nn 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 kk different elements of the array, it will return the position and value of the mm-th among them in the ascending order.

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

You can ask not more than nn queries.

Note that the array aa and number mm 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 aa. You just have to guess mm.

Input

The first line contains two integers nn and kk (1≤k<n≤5001≤k<n≤500) — the length of the array and the number of the elements in the query.

It is guaranteed that number mm satisfies 1≤m≤k1≤m≤k, elements a1,a2,…,ana1,a2,…,an of the array satisfy 0≤ai≤1090≤ai≤109, and all of them are different.

Interaction

You begin the interaction by reading nn and kk.

To ask a question about elements on positions x1,x2,…,xkx1,x2,…,xk, in a separate line output

?? x1x1 x2x2 x3x3 ... xkxk

Numbers in the query have to satisfy 1≤xi≤n1≤xi≤n, and all xixi have to be different. Don't forget to 'flush', to get the answer.

In response, you will receive two integers pospos and aposapos — the position in the array aa of the mm-th in ascending order element among ax1,ax2,…,axkax1,ax2,…,axk, and the element on this position.

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

When you determine mm, output

!! mm

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,mn,k,m (1≤m≤k<n≤5001≤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 nn integers a1,a2,…,ana1,a2,…,an (0≤ai≤1090≤ai≤109) — the elements of the array. They have to be pairwise different.

Example

input

Copy

4 3
4 9
4 9
4 9
1 2

output

Copy

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

Note

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

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int cnt1,cnt2,val1=-1,val2=-1;
int main(){
    int n,k;
    scanf("%d%d",&n,&k);
    for(int i=1;i<=k+1;i++){
        printf("? ");
        for(int j=1;j<=k+1;j++){
            if(i==j)continue;
            printf("%d ",j);
        }
        puts("");
        fflush(stdout);
        int x,y;
        scanf("%d%d",&x,&y);
        if(y==val1||val1==-1){
            cnt1++;
            val1=y;
        }
        else {
            cnt2++;
            val2=y;
        }
    }
    if(val1>val2)
        printf("! %d
",cnt1);
    else 
        printf("! %d
",cnt2);
    return 0;
}