#include <map>
#include <set>
#include <cmath>
#include <queue>
#include <bitset>
#include <vector>
#include <random>
#include <cassert>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <functional>
#include <unordered_map>

using namespace std;

#define rep(i, s, e) for (int i = s; i <= e; ++i)
#define per(i, s, e) for (int i = s; i >= e; --i)
#define file(a) freopen(#a".in", "r", stdin), freopen(#a".out", "w", stdout)
#define pv(a) cout << #a << " = " << a << endl
#define pa(a, l, r) cout << #a " : "; rep(_, l, r) cout << a[_] << " \n"[_ == r]

const int N = 4e5 + 10;
const int L = 30;

int read() {
  int x = 0, f = 1; char c = getchar();
  for (; c < '0' || c > '9'; c = getchar()) if (c == '-') f = -1;
  for (; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + (c - 48);
  return x * f;
}

int n, tc, a[N], o[N], pre[L];

int tot = 1, son[N * L][2], dat[N * L];

void insert(int x, int k) {
  int u = 1;
  dat[u] = k;
  per(i, L - 1, 0) {
    int &v = son[u][x >> i & 1];
    if (!v) v = ++tot;
    u = v, dat[u] = k;
  }
}

int querymx(int x, int k) {
  // cout << "querymx x, k = " << x << ' ' << k << endl;
  int u = 1;
  per(i, L - 1, k + 1) {
    u = son[u][pre[k] >> i & 1];
    // cout << "i, u = " << i << ' ' << u << endl;
  }
  u = son[u][0];
  assert(u);
  per(i, k - 1, 0) {
    if (dat[son[u][~x >> i & 1]]) {
      u = son[u][~x >> i & 1];
    }
    else u = son[u][x >> i & 1];
  }
  return dat[u];
}

int querymn(int x, int k) {
  int u = 1;
  per(i, L - 1, k + 1) {
    u = son[u][pre[k] >> i & 1];
  }
  u = son[u][1];
  assert(u);
  per(i, k - 1, 0) {
    if (dat[son[u][x >> i & 1]]) {
      u = son[u][x >> i & 1];
    }
    else u = son[u][~x >> i & 1];
  }
  return dat[u];
}

int ask(int i) {
  cout << "? " << i << endl;
  cout.flush();
  int res;
  cin >> res;
  return res;
}

void answer(int x) {
  cout << "! " << x << endl;
  cout.flush();
  return;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  cin >> n >> tc;
  rep(i, 1, n) cin >> a[i], o[i] = i;
  rep(i, 1, n) insert(a[i], i);
  sort(o + 1, o + n + 1, [&](int i, int j) {
    return a[i] < a[j];
  });
  rep(d, 0, L - 1) {
    pre[d] = -1;
    rep(i, 1, n - 1) {
      if (((a[o[i + 1]] ^ a[o[i]]) >> d) == 1) {
        // cout << "d, i = " << d << ' ' << i << endl;
        pre[d] = (a[o[i]] >> d) << d;
        break;
      }
    }
  }
  // pa(pre, 0, L - 1);
  while (tc--) {
    int x = 0;
    rep(d, 0, L - 1) {
      if (!~pre[d]) continue;
      int p = querymx(x, d);
      int q = querymn(x, d);
      if (ask(p) != q) x |= 1 << d;
    }
    answer(x);
  }
  return 0;
}