#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using ld = long double;
#define int ll
#define ff first
#define ss second
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()

mt19937 rnd(1329);

int mod;

int fastpow(int a, int b) {
    if (b == 0) return 1;
    int t = fastpow(a, b / 2);
    t = 1ll * t * t % mod;
    if (b % 2) {
        t = 1ll * t * a % mod;
    }
    return t;
}

int lol(int a) {
    return 1 * fastpow(a, mod - 2);
}

bool used[(int)2e5 + 10];

void solve() {
    int n, p;
    cin >> n >> p;
    mod = p;
    vector<int> a(n);
    for (int i = 0; i < n; ++i) cin >> a[i];
    for (auto e : a) used[e] = 1;
    if (used[0] == 0) {
//        cout << "lol ";
        cout << "1 1\n0\n";
        for (auto e : a) used[e] = 0;
        return;
    }
    sort(all(a));
    if (n == 1) {
        for (auto e : a) used[e] = 0;
        cout << p << ' ' << 1 << '\n';
        for (int i = 0; i < p; ++i) cout << i << ' ';
        cout << '\n';
        return;
    }
    int ans = 0;
    while (used[ans]) ans++;
    set<int> anss; anss.insert(1);
    if (ans == 1) anss.insert(0);
    vector<int> nota;
    for (int i = 0; i < n - 1; ++i) for (int j = a[i]; j < a[i + 1]; ++j) nota.push_back(j);
    for (int j = a[n - 1] + 1; j < p; ++j) nota.push_back(j);
    vector<int> ord(p);
    iota(all(ord), 0);
    for (auto x : ord) {
        if (x == 0) continue;
        if (!used[1 * x]) continue;
        bool ok = 1;
        int x = lol(e);
//        cout << x << '\n';
        for (int i = 0; i < 300; ++i) {
            if (ans == 1) break;
            int j = rnd() % (ans - 1) + 1;
            if (used[1ll * j * fastpow(x, mod - 2) % mod]) continue;
            ok = 0;
            break;
        }
        for (int i = 0; i < 300; ++i) {
            if (ans == 1) break;
            int j = nota[rnd() % (nota.size())];
            if (j * x < ans) {
                ok = 0;
                break;
            }
        }
        if (!ok) continue;
        for (int j = 1; j < ans; ++j) {
            if (used[1ll * j * fastpow(x, mod - 2) % mod]) continue;
            ok = 0;
            break;
        }
        if (!ok) continue;
        if (ans == p) {
            anss.insert(x);
            continue;
        }
        if (used[1ll * ans * fastpow(x, mod - 2) % mod]) {
            anss.clear();
            while (ans < p && used[1ll * ans * fastpow(x, mod - 2) % mod]) ans++;
        }
        anss.insert(x);
    }
    cout << anss.size() << ' ' << ans << '\n';
    for (auto e : anss) cout << e << ' '; cout << '\n';
    for (auto e : a) used[e] = 0;
}


signed main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int t;
    cin >> t;
    while (t--) solve();
}

answer.code: In function ‘void solve()’:
answer.code:67:13: error: redeclaration of ‘ll x’
   67 |         int x = lol(e);
      |             ^
answer.code:63:15: note: ‘long long int x’ previously declared here
   63 |     for (auto x : ord) {
      |               ^
answer.code:67:21: error: ‘e’ was not declared in this scope; did you mean ‘std::numbers::e’?
   67 |         int x = lol(e);
      |                     ^
      |                     std::numbers::e
In file included from /usr/include/c++/13/bits/max_size_type.h:37,
                 from /usr/include/c++/13/bits/ranges_base.h:39,
                 from /usr/include/c++/13/bits/ranges_algobase.h:38,
                 from /usr/include/c++/13/bits/ranges_algo.h:38,
                 from /usr/include/c++/13/algorithm:63,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:51,
                 from answer.code:1:
/usr/include/c++/13/numbers:122:27: note: ‘std::numbers::e’ declared here
  122 |   inline constexpr double e = e_v<double>;
      |                           ^