#include<iostream>
#include<cstdio>
#include<algorithm>
#include<vector>
#include<cstring>
#include<queue>
#include<map>
#define LL long long
using namespace std;
const int mod=998244353;
const int Base=23,Base2=27;
inline int lowbit(int x){return x&(-x);}
inline int Jia(int x){return x>=mod?x-mod:x;}
inline int Jian(int x){return x>=0?x:x+mod;}
int KSM(int a,int b){
	int Ans=1;
	while(b){
		if(b&1)Ans=1LL*Ans*a%mod;
		a=1LL*a*a%mod;
		b>>=1;
	}
	return Ans;
}
inline int read(){
	int k=0,ty=1;
	char ch=getchar();
	while(ch<'0'||ch>'9'){
		if(ch=='-')ty=-1;
		ch=getchar();
	}
	while(ch<='9'&&ch>='0'){
		k=k*10+ch-'0';
		ch=getchar();
	}
	return k*ty;
}
int gcd(int a,int b){
	if(!b)return a;
	return gcd(b,a%b);
}
const int maxn=5e5+5;
int rt=1,all=1,ch[maxn][2],Size[maxn],id[maxn],ID[maxn][2],v[maxn],n,m;
int a[maxn],pos[maxn],DFN,ans[maxn],To[maxn];
void Insert(int x){
	int p=rt,c;
	for(int i=2;i>=0;--i){
		if(a[x]&(1<<i))c=1;
		else c=0;
		if(!ch[p][c])ch[p][c]=++all;
//		ID[p][c]=x;
		if(ch[p][0]&&ch[p][1])v[i]=p;
		p=ch[p][c];
	}
	pos[x]=p;To[p]=x;
}
void dfs(int x){
	id[x]=++DFN;Size[x]=1;
	if(ch[x][0])dfs(ch[x][0]);
	if(ch[x][1])dfs(ch[x][1]);
	Size[x]+=Size[ch[x][0]]+Size[ch[x][1]];
}
int Get(int x,int deep){
	if(deep==-1)return To[x];
	if(ch[x][ans[deep]^1])return Get(ch[x][ans[deep]^1],deep-1);
	return Get(ch[x][ans[deep]],deep-1);
}
void Solve(){
	for(int i=0;i<=30;++i){
//		cout<<i<<'\n';
		if(!v[i])ans[i]=0;
		else {
//			cout<<"SHIT\n";
			int p=v[i];
			int p2=Get(ch[p][0],i-1);
//			cout<<p<<' '<<p2<<'\n';
			cout<<"? "<<p2<<'\n';
			cout.flush();
			int t,t2=ch[p][1];
			cin>>t;
//			cout<<t<<'\n';
//			cout<<"FAFAFFA\n";
			if(t==-1){
				ans[i]=1;
				continue;
			}
//			cout<<"F1\n";
			t=pos[t];
//			cout<<"F2\n";
			if(id[t2]<=id[t]&&id[t2]+Size[t2]>id[t])ans[i]=0;
			else ans[i]=1;
		}
	}
//	cout<<"FAFAF\n";
	int Ans=0;
	for(int i=30;i>=0;--i){
//		cout<<ans[i]<<'\n';
		Ans=Ans+(ans[i]<<i);
	}
	cout<<"! "<<Ans<<'\n';
	cout.flush();
}
int main(){
//	n=read();m=read();
	std::ios::sync_with_stdio(false);
//	cin.tie(0);
	cin>>n>>m;
//	cout<<n<<' '<<m<<'\n';
	for(int i=1;i<=n;++i){
		cin>>a[i];
		Insert(i);
	}
//	cout<<"AFA\n";
	dfs(rt);
//	cout<<"FAF\n";
	for(int i=1;i<=m;++i){
		Solve();
	}
	cout.flush();
	return 0;
}