#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fast ios_base::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL)

int main(){
    fast;

    ll t,tcno=0;cin>>t;
    while(t--){
        ll n,m;cin>>n>>m;
        ll a[n];
        ll b = 0;
        for(ll i=0;i<n;++i){
            cin>>a[i];
            //b = max(b, (ll)log2l(a[i])+1);
            for(ll j=50;j>=0;--j){
                if(a[i] & (1ll<<j)){
                    b = max(b, 1+j);
                    break;
                }
            }
        }

        ll ans = 0;
        for(ll i=b-1;i>=0;--i){
            ll tot = 0;
            for(ll j=0;j<n;++j){
                if(a[j] & (1ll << i)){
                    ++tot;
                }
            }
            //cout<<"\nres="<<tot<<endl;
            if(tot>n/2){
                ans += 1ll << i;
            }
        }
        ll r = 0;
        for(ll i=0;i<n;++i){
            r+= ans ^ a[i];
        }
        if(r>m){
            cout<<"Case #"<<++tcno<<": "<<-1<<endl;
            continue;
        }
        //cout<<"preans"<<ans<<endl;
        for(ll i=b-1;i>=0;--i){
            if((ans & (1ll << i))==0){
                ll res = 0;
                ll x = ans + (1ll <<i);
                for(ll j=0;j<n;++j){
                    res += x ^ a[j];
                }
                if(res<=m){
                    ans += (1ll << i);
                }
            }
        }
        cout<<"Case #"<<++tcno<<": "<<ans<<endl;
    }
    return 0;
}