#include<bits/stdc++.h>
using namespace std;
using LL=long long;
using ULL=unsigned long long;
#define rep(i,n) for(int i=0; i<(n); i++)

const LL result_impossible = -1000000000000;

LL testcase(){
  LL N,A,W,K; cin>>N>>A>>W>>K;

  if(A<K-1 && W<N-K+1) return result_impossible;

  if(N!=K){
    if(A<K-1) return -1;
    return (A-(K-1)) / K;
  }
	
  LL diff = (W+N-1)/N;
  LL low = -diff*(diff+1)/2;
  LL low_width = W-(diff-1)*K;
  if(A >= low_width*diff + (N-1)){
    // low+diff <= ans
    A -= low_width*diff + (N-1);
    return low+diff + A/K;
  }
  if(A >= low_width-1){
    // low <= ans < low+diff
    A-=low_width-1;
    return min(low + A/low_width, low+diff-1);
  }
  // ans < low
  LL ans=low-(diff+1);
  ans+=min(diff,A);
  return ans;
}

int main(){
  int T; cin>>T;
  rep(t,T){
    LL ans=testcase();
    if(ans==result_impossible) cout<<":("<<endl;
    else cout<<ans<<endl;
  }
  return 0;
}