#include <bits/stdc++.h>
#define IOS ios::sync_with_stdio(0), cin.tie(0)
#define int long long
//#define endl '\n'
#define lowbit(x) (x)&(-x)
#define pii pair<int,int>
#define all(s) s.begin(), s.end()
#define ls(x) (x<<1)
#define rs(x) (x<<1|1) 
#define here system("pause")
using namespace std;

const int N = 4e5+5;
const int mod = 1e9+7;
const int INF = 1e15+7;
const double eps = 1e-6;
inline int pow(int a, int b, int p){ int res = 1%p; while(b){ if(b&1) res=res*a%p; a=a*a%p, b>>=1;} return res;}
inline int inv(int a, int p){ return pow(a,p-2,p)%p;}
int n, m, tot;
int a[N], ch[N*31][2], dep[N*31], id[N*31];
int wh[31] = {-1};//用于存储具有两个不同子节点（即0和1分支都存在）的节点的索引，如果不存在则为-1。

inline int ask(int x){
	cout << "? " << x << endl;
	cin >> x;
	return x;
}

inline int insert(int x){
	int p = 0;
	for(int i=29;i>=0;i--){
		int j = x>>i&1;
		if(!ch[p][j]) ch[p][j] = ++tot, dep[p] = i;
		p = ch[p][j];
	}
	return p;
}

inline void sol(){
	cin >> n >> m;
	for(int i=1;i<=n;i++){
		cin >> a[i];
		int p = insert(a[i]);
		id[p] = i;
	}
	
	for(int i=0;i<30;i++) wh[i] = -1;
	
	for(int i=0;i<tot;i++){
		if(ch[i][0] && ch[i][1]) wh[dep[i]] = i;
	}
	
	while(m--){
		int res = 0;
		for(int i=0;i<30;i++){
			if(~wh[i]){
				int l = ch[wh[i]][0], r = ch[wh[i]][1];
				for(int j=i-1;j>=0;j--){
					if(ch[l][!((res>>j)&1)]) l = ch[l][!((res>>j)&1)];
					else l = ch[l][(res>>j)&1];
					
					if(ch[r][(res>>j)&1]) r = ch[r][(res>>j)&1];
					else r = ch[r][!((res>>j)&1)];
				}
				
				if(ask(id[l])!=id[r]){
					res |= 1<<i;
				}
			}
		}
		cout << "! " << res << endl;
	} 
}


signed main(){
	IOS;
	int tc = 1;
	while(tc--){
		sol();
	}
	return 0;
}