#include <bits/stdc++.h>

using namespace std;

#define SZ(x) ((int)((x).size()))
#define lb(x) ((x) & (-(x)))
#define bp(x) __builtin_popcount(x)
#define bpll(x) __builtin_popcountll(x)
#define mkp make_pair
#define pb push_back
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, int> pli;
typedef pair<ll, ll> pll;
typedef pair<double, int> pdi;

const int MAXN = 4e5 + 10;

struct Trie01 {
    int cnt_id;
    int tr[MAXN * 30][2];
    int ins_id[MAXN * 30];
    int pos[30];

    void insert(int x, int id) {
        int u = 0;
        for (int i = 29; i >= 0; i--) {
            int dig = (x >> i) & 1;
            if (!tr[u][dig]) {
                tr[u][dig] = ++cnt_id; 
            }
            u = tr[u][dig];
        }
        ins_id[u] = id;
    }
    void dfs(int u, int d) {
        int son = 0;
        if (tr[u][0]) {
            dfs(tr[u][0], d - 1);
            son++;
        }
        if (tr[u][1]) {
            dfs(tr[u][1], d - 1);
            son++;
        }
        
        if (son == 2) {
            pos[d] = u;
        }
    }
    void init() {
        memset(pos, -1, sizeof(pos));
        dfs(0, 29);
    }
} T;

void solve() {
    int n, q;
    cin >> n >> q;
    vector a(n + 1, 0);
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        T.insert(a[i], i);
    }
    T.init();

    auto ask = [&](int p) -> int {
        cout << "? " << p << '\n';
        cout.flush(); 
        int res;
        cin >> res;
        return res;
    };

    while (q--) {
        int ans = 0;
        for (int i = 0; i <= 29; i++) {
            if (T.pos[i] == -1) {
                continue;
            }
            int x = T.tr[T.pos[i]][0];
            int y = T.tr[T.pos[i]][1];
            for (int j = i - 1; j >= 0; j--) {
                int dig = (ans >> j) & 1;
                if (T.tr[x][!dig]) {
                    x = T.tr[x][!dig];
                }
                else {
                    x = T.tr[x][dig];
                }

                if (T.tr[y][dig]) {
                    y = T.tr[y][dig];
                } 
                else {
                    y = T.tr[y][!dig];
                }
            }

            int p = ask(T.ins_id[x]);
            if (p != T.ins_id[y]) {
                ans |= (1 << i);
            }
        }
        cout << "! " << ans << '\n';
        cout.flush();
    }
}

int main() {
    // ios::sync_with_stdio(false);
    // cin.tie(0), cout.tie(0);
    int T = 1;
    while (T--) solve();
    return 0;
}