#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
#include <fstream>
#include <utility>
#include <functional>
#include <time.h>
#include <stack>
#include <array>
#include <list>
#include <atcoder/all>
#define popcount __builtin_popcount
using namespace std;
using namespace atcoder;
typedef long long ll;
typedef pair<int, int> P;

int main()
{
    int t; cin>>t;
    while(t--){
        ll n, a, w, k;
        cin>>n>>a>>w>>k;
        if(k<n){
            if(a>=k-1){
                cout<<(a-(k-1))/k<<endl;
            }else if(w>=n-(k-1)){
                cout<<-1<<endl;
            }else{
                cout<<":("<<endl;
            }
            continue;
        }
        if(w==0 && a<n-1){
            cout<<":("<<endl;
            continue;
        }
        using lll=__int128_t;
        ll l=-1e18, r=1e9;
        while(r-l>1){
            ll m=(l+r)/2;
            ll l1=-1, r1=2e9;
            while(r1-l1>1){
                ll m1=(l1+r1)/2;
                if(m1*(m1+1)/2>=-m){
                    r1=m1;
                }else{
                    l1=m1;
                }
            }
            if(r1*(r1+1)/2+m>a){
                r1--;
                if(r1<0){
                    r=m;
                    continue;
                }
            }
            r1=min(r1, w);
            ll a1, x1;
            if(-r1*(r1+1)/2<m){
                a1=a-(m+r1*(r1+1)/2);
                x1=m+1;
                ll w1=w-r1;
                ll p=w1%(n-1);
                ll q=w1/(n-1);
                lll s=(lll)max(0ll, x1+(q+1)*(q+2)/2)*p+(lll)max(0ll, x1+(q+1)*q/2)*(n-1-p);
                if(s<=a1){
                    l=m;
                    continue;
                }
                r1--;
                if(r1<0){
                    r=m;
                    continue;
                }
            }
            a1=a;
            x1=-r1*(r1+1)/2+1;
            ll w1=w-r1;
            ll p=w1%(n-1);
            ll q=w1/(n-1);
            lll s=(lll)max(0ll, x1+(q+1)*(q+2)/2)*p+(lll)max(0ll, x1+(q+1)*q/2)*(n-1-p);
            if(s<=a1) l=m;
            else r=m;
        }
        cout<<l<<endl;
    }
    return 0;
}