#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#define pll pair <ll,ll>
#define fi first
#define se second
#define sz(a) (ll((a).size()))
#define BIT(mask,i) (((mask) >> (i))&1LL)
#define MASK(i) (1LL << (i))
mt19937_64 rng(1);
mt19937_64 rng2(chrono::steady_clock::now().time_since_epoch().count());
ll random2(ll l,ll r){
    return rng2()%(r-l+1)+l;
}
ll random(ll l,ll r){
    return rng()%(r-l+1)+l;
}
ll myrandom(ll i){
    return rng()%i;
}
ll base1=998244353, base2=1e9+7;
ll match[505][505];
const ll MOD = 10000121;
ll random_val[MOD];

ll f(ll x,ll y,ll n){
    ll val = ((random_val[x]%MOD+500)*(2*n+5)+random_val[y]%MOD+1+69420)*45;
    val += MOD/2;
    val = val%MOD;
    val = val*val%MOD;
    return random_val[val]%(2*n+1);
}
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    for (ll i = 0;i < MOD;i ++)random_val[i] = rng();
    ll t, type; cin >> t >> type;
    auto assistant_small=[&](ll n)
    {
        ll sum=0, Mod=n*2+1;
        vector <ll> a(n);
        for (ll& i:a) cin >> i, sum=(sum+i)%Mod;
        for (ll i=0; i<n; i++)
            for (ll j=0; j<n; j++)
                if (i!=j && match[a[i]][a[j]]==sum)
                {
                    cout << a[i] << " " << a[j] << "\n";
                    return;
                }
    };
    auto magician_small=[&](ll n)
    {
        ll Mod=n*2+1, fa1, fb1, fa2, fb2; cin >> fa1 >> fb1 >> fa2 >> fb2;
        ll sum=match[fa1][fb1]+match[fa2][fb2];
        sum=((n*2+1-sum)%Mod+Mod)%Mod; cout << sum << "\n";
    };
    auto assistant=[&](ll n)
    {
        ll sum=0, fa=0, fb=0, Mod=n*2+1;
        vector <ll> a(n);
        for (ll& i:a) cin >> i, sum=(sum+i)%Mod;
        sort(a.begin(), a.end());
        for (ll i=0; i<n; i++)
            for (ll j=i+1; j<n; j++)
            {
                if ((a[i]+a[j])%Mod==sum) fa=a[i], fb=a[j];
                if ((a[i]+a[j]+n)%Mod==sum) fa=a[j], fb=a[i];
            }
        cout << fa << " " << fb << "\n";
    };
    auto magician=[&](ll n)
    {
        ll Mod=n*2+1, fa1, fb1, fa2, fb2; cin >> fa1 >> fb1 >> fa2 >> fb2;
        ll sum=(fa1<fb1?fa1+fb1:fa1+fb1+n)+(fa2<fb2?fa2+fb2:fa2+fb2+n);
        sum=((n*2+1-sum)%Mod+Mod)%Mod; cout << sum << "\n";
    };
    while (t--)
    {
        ll n; cin >> n;
        if (n <= 6){
            auto init=[&](ll a, ll b)
            {
                for (ll s=0; s<=n*2; s++)
                    match[(a+s)%(n*2+1)][(b+s)%(n*2+1)]=s;
            };
            if (n<=500)
            {
                if (n%2==0)
                {
                    for (ll i=n*2; i>=n+2; i--)
                        init(i, n*2+1-i);
                    init(0, n*2), init(0, 1), init(n*2-3, n+1);
                    init(n, 2), init(n, n*2-1), init(4, n+1);
                }
                else
                {
                    for (ll i=1; i<=n-1; i++)
                        init(i, n*2+1-i);
                    init(0, n*2), init(0, 1), init(n, 2);
                    init(n, n*2-1), init(4, n+1), init(n*2-3, n+1);
                }
                if (type<=2) assistant_small(n);
                else magician_small(n);
            }
            else
            {
                if (type<=2) assistant(n);
                else magician(n);
            }
        }
        else{
            if (type==3){
                ll a,b,c,d;
                cin>>a>>b>>c>>d;
                ll res = -(f(a,b,n)+f(c,d,n));
                res = (res%(2*n+1)+2*n+1)%(2*n+1);
                cout<<res<<'\n';
            }
            else{
                vector <ll> a(n);
                ll sum = 0;
                for (auto &x:a){cin>>x;sum = (sum+x)%(2*n+1);}
                ll u,v;
                u = random2(0,sz(a)-1);
                v = random2(0,sz(a)-1);
                while ((u == v || f(a[u],a[v],n) != sum)){
                    u = random2(0,sz(a)-1);
                    v = random2(0,sz(a)-1);
                }
                cout<<a[u]<<' '<<a[v]<<'\n';
            }
        }
    }
}