#include <bits/stdc++.h>
#define ll long long
#define ls son[x][0]
#define rs son[x][1]

using namespace std;
const ll N=801010;
const ll qwq=N*32;

inline ll read() {
    ll sum = 0, ff = 1; char c = getchar();
    while(c<'0' || c>'9') { if(c=='-') ff = -1; c = getchar(); }
    while(c>='0'&&c<='9') { sum = sum * 10 + c - '0'; c = getchar(); }
    return sum * ff;
}

ll n,m;
ll a[N];
ll son[qwq][2],tot,dep[qwq];
ll id[qwq];
ll xiong1[N],xiong2[N];

inline ll ask(ll cl,ll x,ll now,ll k) {   // 1 : max

	// cout<<"cl = "<<cl<<" x = "<<x<<" k = "<<k<<"\n";
	for(;k>=0;k--) {
		ll c = (now>>k)&1;
		if(cl==1) {
			if(son[x][c^1]) x = son[x][c^1];
			else            x = son[x][c];
		}
		else {
			if(son[x][c]) x = son[x][c];
			else          x = son[x][c^1];
		}
	}
	// cout<<"id = "<<id[x]<<"\n";
	return id[x];
}

int main() {
	n = read(); m = read();
	dep[0] = 30;
	for(ll i=1;i<=n;i++) {
		a[i] = read();
		ll now = 0;
		for(ll k=29;k>=0;k--) {
			ll c = (a[i]>>k)&1;
			if(!son[now][c]) son[now][c] = ++tot, dep[tot] = k;
			now = son[now][c];
		}
		id[now] = i;
	}
	for(ll i=0;i<=tot;i++) {
		if(son[i][0] && son[i][1]) {
				xiong1[ dep[i]-1 ] = son[i][0], xiong2[ dep[i]-1 ] = son[i][1];
		}
	}
	while(m--) {
		ll now = 0;
		for(ll k=0;k<=29;k++) {
			if(!xiong1[k]) continue;
			// cout<<xiong1[k]<<" "<<xiong2[k]<<" k = "<<k<<endl;
			ll A = ask(1,xiong1[k],now,k-1);
			ll B = ask(0,xiong2[k],now,k-1);
			cout<<"? "<<A<<"\n";
			fflush(stdout);
			ll C = read();
			if(C!=B) now |= (1ll<<k);
		}
		cout<<"! "<<now<<"\n";
		fflush(stdout);
	}

	return 0;
}


/*

31 1
0 1 2 4 8    16 32 64 128 256   
512 1024 2048 4096 8192    16384 32768 65536 131072 262144    
524288 1048576 2097152 4194304 8388608    16777216 33554432 67108864 134217728 268435456 536870912

*/