#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
#define FOR() ll le=e[u].size();for(ll i=0;i<le;i++)
#define QWQ cout<<"QwQ\n";
#define ll long long
#include <vector>
#include <queue>
#include <map>

typedef long double db;
using namespace std;
const ll N=501010;
const ll qwq=303030;
const ll inf=0x3f3f3f3f3f;
const db eps = 1e-8;

inline ll read() {
    ll sum = 0, ff = 1; char c = getchar();
    while(c<'0' || c>'9') { if(c=='-') ff = -1; c = getchar(); }
    while(c>='0'&&c<='9') { sum = sum * 10 + c - '0'; c = getchar(); }
    return sum * ff;
}

ll T;
ll n,p;
ll vis[N];
ll a[N],d[N],num;
ll ans;
ll st[N],cnt;
ll ni[N] = {0,1};

void chushihua() {
    cnt = num = ans = 0;
    for(ll i=0;i<=p;i++) vis[i] = 0;
}

int main() {
    T = read();
    while(T--) {
        chushihua();
        n = read(); p = read();
        for(ll i=2;i<p;i++) ni[i] = p - (p/i) * ni[p%i] %p;
        for(ll i=1;i<=n;i++) vis[read()] = 1;

        if(!vis[0]) { cout<<"1 1\n0\n"; continue; }
        if(n==p) {
            cout<<p-1<<" "<<p<<"\n";
            for(ll i=1;i<p;i++) cout<<i<<" \n"[i==p-1];
            continue;
        }

        ll sq = sqrt(p);

        if(p-n<=sq) {
            for(ll i=1;i<p;i++) if(!vis[i]) d[++num] = i;
            for(ll c=1;c<p;c++) {
                ll mi = inf;
                for(ll i=1;i<=num;i++) mi = min(mi,d[i]*c%p);
                if(mi>ans) {
                    ans = mi;
                    st[cnt=1] = c;
                }
                else if(mi==ans) {
                    st[++cnt] = c;
                }
            }
        }

        else {
            for(ll c=1;c<p;c++) {
                ll res = 0;
                for(ll i=1;i<p;i++) {
                    if(!vis[i*ni[c]%p]) { res = i; break; }
                }
                if(res>ans) {
                    ans = res;
                    st[cnt=1] = c;
                }
                else if(res==ans) {
                    st[++cnt] = c;
                }
            }
        }

        cout<<cnt<<" "<<ans<<"\n";
        for(ll i=1;i<=cnt;i++) cout<<st[i]<<" \n"[i==cnt];
    }
    return 0;
}
/*

5


*/