#include <bits/stdc++.h>
using namespace std;

#define all(a) a.begin(), a.end()
const int N = 400010, M = 31;

int ch[N * M][M], idx, a[N], pre[N];
int ed[N * M], node[M];

void insert (int x, int v) {
    int p = 0;
    for (int i = M - 1, s = 0; i >= 0; i --) {
        int j = x >> i & 1;
        s |= j << i;
        int& u = ch[p][j];
        if (!u) {
            u = ++ idx;
            pre[u] = s;
        }
        if (node[i] == 0 && ch[p][0] && ch[p][1]) {
            node[i] = p;
        }
        p = u;
    }
    ed[p] = v;
}

int query (int x) {
    cout << "? " << x << endl;
    int res;
    cin >> res;
    return res;
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	
	int n, m;
	cin >> n >> m;
	
	for (int i = 1; i <= n; i ++) {
	    int x;
	    cin >> x;
	    a[i] = x;
	    insert(x, i);
	}
	
	while (m --) {
	    int ans = 0;
	    for (int i = 0; i < M; i ++) {
	        int& x = node[i];
	        if (!x) continue;
	        
	        function<int(int, int)> get_max = [&](int p, int j) {
	            if (j == -1) {
	                return ed[p];
	            }
	            if (!ch[p][1]) {
	                return get_max(ch[p][0], j - 1);
	            }
	            if (!ch[p][0]) {
	                return get_max(ch[p][1], j - 1);
	            }
	            if (ans >> j & 1 ^ 1) {
	                return get_max(ch[p][1], j - 1);
	            }
	            return get_max(ch[p][0], j - 1);
	        };
	        
	        int p = get_max(ch[x][0], i - 1);
	        int q = query(p);
	        if (q == -1 || (a[q] ^ pre[ch[x][1]]) >= (1 << i)) {
	            ans |= 1 << i;
	        }
	    }
	    cout << "! " << ans << endl;
	}
    
	return 0;
}