#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef unsigned long long ull;

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll myRand(ll B) {
	return (ull)rng() % B;
}

int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	int q; cin >> q;
	while(q--){
		ll n,a,w,k; cin >> n >> a >> w >> k;
		if(k==1){
			if(a)printf("%lld\n",a);
			else{
				if(w<n-1){
					printf(":(\n");
				}
				else{
					printf("0\n");
				}
			}
		}
		else if(n==k){
			if(w==0){
				if(a<n-1){
					printf(":(\n");
				}
				else{
					printf("0\n");
				}
			}
			else{
				ll L=-1,R=w; // 最下位が不正解する回数
				while(R-L>1){
					ll mid=(L+R)/2;
					ll tmp=(w-mid)/(n-1);
					ll m=tmp*(tmp+1)/2*(n-1);
					ll u=w-tmp-tmp*(n-1);
					ll uu=(n-1)-u;
					ll aa=((mid*(mid+1)/2-1)>=m+(tmp+1)?0:(mid*(mid+1)/2-1)-m-(tmp+1));
					aa*=u;
					ll aaa=((mid*(mid+1)/2-1)>=m?0:(mid*(mid+1)/2-1)-m);
					aaa*=uu;
					if(aa+aaa<=a){
						R=mid;
					}
					else{
						L=mid;
					}
				}
				printf("%lld\n",-R*(R+1)/2);
			}
		}
		else{
			if(a==0){
				if(w>=1+(n-k)){
					printf("-1\n");
				}
				else{
					printf(":(\n");
				}
			}
			else{
				ll L=-1,R=2e9;
				while(R-L>1){
					ll mid=(L+R)/2;
					if((k-1)*(mid+1)+mid<=a)L=mid;
					else R=mid;
				}
				if(L==-1)printf(":(\n");
				else printf("%lld\n",L);
			}
		}
	}
}