#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
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
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;
}

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/(k-1)+(i<a%(k-1));

            ll lw=0,hi=1000000ll,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]=t+1;

            vector<ll> y(n);
            sort(ALL(v));
            sort(ALL(p));
            rep(i,n) y[i]=p[i]-v[i]*(v[i]+1)/2;
            sort(ALL(y));
            if(y[0]!=y[1]){
                cout<<y[0]<<endl;
            }else{
                if(p[0]){
                    p[0]--;
                    cout<<p[0]-v[0]*(v[0]+1)/2<<endl;
                }else if(v.back()){
                    v[0]++;
                    cout<<p[0]-v[0]*(v[0]+1)/2<<endl;
                }else{
                    cout<<":("<<endl;
                }
            }
        }
    }
    return 0;
}