#include<bits/stdc++.h>
// #include<atcoder/all>
// #include<boost/multiprecision/cpp_int.hpp>

using namespace std;
// using namespace atcoder;
// using bint = boost::multiprecision::cpp_int;
using ll = long long;
using ull = unsigned long long;
using P = pair<int,int>;
#define rep(i,n) for(ll i = 0;i < (ll)n;i++)
#define ALL(x) (x).begin(),(x).end()
#define MOD 1000000007



int main(){
  
  int T;
  cin >> T;
  while(T--){
    int n,A,W,K;
    cin >> n >> A >> W >> K;
    if(K != n && K != 1){
      ll l = -1,r = MOD;
      while(r-l > 1){
        ll mid = (l+r)/2;
        bool ok = true;
        if((mid+1)*(K-1) + mid > A)ok = false;
        if(ok)l = mid;
        else r = mid;
      }
      if(l == -1){
        if(W >= n - K + 1)l = -1;
        else l = -MOD;
      }

      if(l != -MOD)cout << l << "\n";
      else cout << ":(\n";

    }else if(K == 1){
      cout << A << "\n";
    }else if(K == n){
      ll l = 0,r = A+1;
      ll res = -1ll*MOD*MOD;
      while(r-l > 1){
        ll mid = (l+r)/2;
        ll mn = (A-mid)/(n-1),mx = (A-mid+n-2)/(n-1);
        ll l2 = -1,r2 = W;
        while(r2-l2 > 1){
          ll mid2 = (l2 + r2)/2;
          ll k = W - mid2;
          ll s = k/(n-1),t = (k+n-2)/(n-1);
          if(mid - mid2*(mid2+1)/2 < min(mn - s*(s+1)/2,mx - t*(t+1)/2))r2 = mid2;
          else l2 = mid2;
        }
        ll k = W - r2;
        ll s = k/(n-1),t = (k+n-2)/(n-1);
          
        if(mid - r2*(r2+1)/2 < min(mn - s*(s+1)/2,mx - t*(t+1)/2)){
          res = max(res,mid - r2*(r2+1)/2);
          l = mid;
        }else{
          r = mid;
        }

      }
      if(res != -1ll*MOD*MOD)cout << res << "\n";
      else cout << ":(\n";
    }
  }


  return 0;
}