#include<bits/stdc++.h>

using namespace std;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define pf push_front
#define LC k << 1
#define RC k << 1 | 1
#define IO cin.sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define all(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
#define rep(i, a, n) for (int i = a; i < n; i++)
#define repn(i, a, n) for (int i = a; i <= n; i++)
#define per(i, a, n) for (int i = (n) - 1; i >= a; i--)
#define pern(i, a, n) for (int i = n; i >= a; i--)

typedef long long LL;
typedef long double LD;
typedef unsigned long long ull;
typedef pair<int, int> PII;
typedef pair<int, LL> PIL;
typedef pair<LL, int> PLI;
typedef pair<double, double> PDD;
typedef pair<ull, ull> PUU;
typedef pair<LL, LL> PLL;

const int N = 410000;
const int M = 1100000;
const int mod = 1e9 + 7;
const int inf = 1e9;
const LL INF = 1e18;
const double eps = 1e-9;

mt19937_64 Rand((unsigned long long)new char);
#define rand Rand

bool valid[N];
int primm, prim[N], nc, pr[N];
void getPrime(int n) {
	memset(valid, true, sizeof(valid));
	repn(i, 2, n) if (valid[i]) {
		prim[++primm] = i;
		repn(j, 2, n / i) valid[i * j] = 0;
	}
}
LL pow_mod(LL a, LL e, LL p) {
	LL res = 1;
	for (; e; a = a * a % p, e >>= 1) if (e & 1) res = res * a % mod;
	return res;
}
void cal(LL n) {
	LL t = n, a;
	nc = 0;
	for (int i = 1; prim[i] * prim[i] <= n; i++) {
		if (n % prim[i] == 0) {
			pr[++nc] = prim[i];
			while (n % prim[i] == 0) n /= prim[i];
		}
	}
	if (n > 1) pr[++nc] = n;
}
LL findprimitiveroot(LL P){
	if (P == 2) return 1;
	LL t, g, root;
	cal(P - 1);
	for (g = 2; g < P; g++) {
		bool flag = true;
		repn(i, 1, nc) {
			t = (P - 1) / pr[i];
			if (pow_mod(g, t, P) == 1) {
				flag = false;
				break;
			}
		}
		if (flag) {
			root = g;
			return root;
		}
	}
}
#define complex my_complex
const int MAXN = 1 << 21;
const double PI = acos(-1.0);
struct complex {
	double r, i;
	complex(double _r = 0.0, double _i = 0.0) { r = _r; i = _i;}
	complex operator + (const complex &b) { return complex(r + b.r, i + b.i);}
	complex operator - (const complex &b) { return complex(r - b.r, i - b.i);}
	complex operator * (const complex &b) { return complex(r * b.r - i * b.i, r * b.i + i * b.r);}
	complex conj() {return complex(r, -i);}
};
complex W[2][MAXN * 2];
complex fa[MAXN], fb[MAXN];
void init() {
	for (int h = 2; h <= MAXN; h <<= 1) {
		for (int d = 0; d < h / 2; d++) {
			W[0][h + d] = complex(cos(2 * d * PI / h), sin(2 * d * PI / h));
			W[1][h + d] = complex(cos(-2 * d * PI / h), sin(-2 * d * PI / h));
		}
	}
}
void change(complex y[], int len) {
	int i, j, k;
	for (i = 1, j = len / 2; i < len - 1; i++) {
		if (i < j) swap(y[i], y[j]);
		k = len / 2;
		while (j >= k) j -= k, k /= 2;
		if (j < k) j += k;
	}
}
void fft(complex y[], int len, int type) {
	change(y, len);
	for (int h = 2; h <= len; h <<= 1) {
		for (int j = 0; j < len; j += h) {
			for (int k = j, d = 0; k < j + h / 2; k++, d++) {
				complex w;
				if (type == 1) w = W[0][h + d];
				else w = W[1][h + d];
				complex u = y[k], t = w * y[k + h / 2];
				y[k] = u + t;
				y[k + h / 2] = u - t;
			}
		}
	}
	if (type == -1) rep(i, 0, len) y[i].r /= len, y[i].i /= len;
}
int T, n, flag, p, a[N], rt, prj[N], arr[N], b[N], c[N], d[N];
int check(int len) {
	int l = 1;
	while (l <= 4 * p) l *= 2;
	repn(i, 0, p) c[i] = 0;
	rep(i, 0, len) c[prj[i + 1]] = 1;
	reverse(c, c + p - 1);
	rep(i, 0, l) {
		if (i <= p + p) fa[i] = complex(b[i], 0);
		else fa[i] = complex(0, 0);
		if (i <= p) fb[i] = complex(c[i], 0);
		else fb[i] = complex(0, 0);
	}
	fft(fa, l, 1), fft(fb, l, 1);
	rep(i, 0, l) fa[i] = fa[i] * fb[i];
	fft(fa, l, -1);
	int flag = 0;
	repn(i, 0, p) d[i] = 0;
	rep(i, 0, p - 1) {
		int v = (int)(fa[i + p - 2].r + 0.1);
		int id1 = (p - 1 + i) % (p - 1);
		if (v == len) d[id1] = flag = 1;
	}
	return flag;
}
int main() {
	IO;
	getPrime(N - 1);
	init();
	cin >> T;
	while (T--) {
		cin >> n >> p;
		flag = 0;
		repn(i, 1, n) {
			cin >> a[i];
			if (a[i] == 0) flag = 1;
		}
		if (!flag) {
			cout << "1 1\n0\n";
			continue;
		}
		rt = findprimitiveroot(p);
		prj[1] = 0;
		arr[0] = 1;
		LL cur = 1;
		rep(i, 1, p - 1) cur = cur * rt % p, prj[cur] = i, arr[i] = cur;
		repn(i, 0, p + p) b[i] = 0;
		repn(i, 1, n) if (a[i] != 0) {
			int t = prj[a[i]];
			b[t] = b[t + p - 1] = 1;
		}
		int l = 1, r = p - 1, ans = 0;
		while (l <= r) {
			int mid = (l + r) / 2;
			if (check(mid)) l = mid + 1, ans = mid;
			else r = mid - 1;
		}
		if (ans == 0) {
			cout << p << " " << 1 << "\n";
			rep(i, 0, p) cout << i << " \n"[i == p - 1];
			continue;
		}
		check(ans);
		vector<int> v;
		rep(i, 0, p - 1) if (d[i] == 1) {
			v.pb(arr[i]);
		}
		sort(all(v));
		cout << v.size() << " " << ans + 1 << "\n";
		rep(i, 0, v.size()) cout << v[i] << " \n"[i == SZ(v) - 1];
	}
	return 0;
}