#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 1000000007

int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;
 
template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}

// 2^127 = 170141183460469231731687303715884105728 ~ 10^38
 
ostream &operator<<(ostream &os,const __int128 &n){
    if(n==0){
        os<<0;
        return os;
    }
    __int128 num=n;
    bool neg=false;
    if(num<0)neg=true,num=-num;
    string res="";
    while(num>0){
        res.push_back('0'+num%10);
        num/=10;
    }
    if(neg) res.push_back('-');
    reverse(begin(res),end(res));
    os<<res;
    return os;
}

istream &operator>>(istream &is,__int128 &n){
    string s;
    is>>s;
    int idx=0;
    bool neg=false;
    if(s[0]=='-')neg=true,idx++;
    n=0;
    for(;idx<(int)s.size();idx++){
        n=10*n+s[idx]-'0';
    }
    if(neg) n=-n;
    return is;
}

__int128 abs128(__int128 x){
    return x<0?-x:x;
}
 
__int128 gcd128(__int128 a,__int128 b){
    if(a==0) return b;
    if(b==0) return a;
    return b>0?gcd128(b,a%b):a;
}
using ll=__int128;


const int INF=1000000000;
const ll LINF=1001002003004005006ll;

signed main(){
    int q;cin>>q;
    while(q--){
        int n;cin>>n;
        ll a,w,k;cin>>a>>w>>k;


        if(k==1){
            cout<<a<<endl;
            continue;
        }

        auto f=[&](ll mid){
            ll AC=a,WA=w;

            vector<ll> v(k-1);
            AC-=mid;

            rep(i,k-1) v[i]=AC/(k-1)+(i<AC%(k-1));

            ll mi=*min_element(ALL(v));
            if(mi>mid) return true;
            return false;            
        };


        if(k<n){
            ll lw=-LINF,hi=a,res=-LINF;
            while(lw<=hi){
                ll mid=(lw+hi)/2;
                if(f(mid)) res=mid,lw=mid+1;
                else hi=mid-1;
            }
            if(res<w) cout<<":("<<endl;
            else cout<<res<<endl;
        }else{
            ll wm=w;
            vector<ll> p(n);
            rep(i,n) p[i]=a/n+(i<a%n);

            ll lw=0,hi=w,t;
            while(lw<=hi){
                ll m=(lw+hi)/2;
                if(m*(m+1)/2*n<=w) t=m,lw=m+1;
                else hi=m-1;
            }

            vector<ll> v(n,0);
            rep(i,n) v[i]=t;
            w-=t*(t+1)/2*n;
            rep(i,w) v[i%n]++;

            ll ans=-LINF;

            auto unko=[&](){
                vector<tuple<ll,ll,ll>> y(n);
                rep(i,n) y[i]=make_tuple(p[i]-v[i]*(v[i]+1)/2,p[i],v[i]);
                sort(ALL(y));
                if(get<0>(y[0])!=get<0>(y[1])){
                    chmax(ans,get<0>(y[0]));
                }else{
                    if(get<1>(y[0])){
                        chmax(ans,get<0>(y[0])-1);
                    }else{
                        ll mugen=0;
                        for(int i=1;i<n;i++){
                            chmax(mugen,get<2>(y[i]));
                        }
                        if(mugen){
                            ll hoge=get<2>(y[0])+1;
                            chmax(ans,get<1>(y[0])-hoge*(hoge+1)/2);
                        }
                    }
                }
            };

            sort(ALL(v));
            sort(ALL(p));

            unko();

            reverse(ALL(v));
            unko();

            reverse(ALL(p));
            unko();

            reverse(ALL(v));
            unko();

            if(ans<=-LINF) cout<<":("<<endl;
            else cout<<ans<<endl;
        }
    }
    return 0;
}