#include<bits/stdc++.h>
using namespace std;
#define ll long long
int t;
ll x,y,p,q;
inline ll exgcd(ll a,ll b,ll &num3,ll &num4){
	if(!b){
		num3=1,num4=0;
		return a;
	}ll r=exgcd(b,a%b,num3,num4),tmp=num3;
	num3=num4,num4=tmp-a/b*num4;
	return r;
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0),cout.tie(0);
	cin>>t;
	while(t--){
		cin>>x>>y>>p>>q;
		ll ans=2e18,pos1=1,pos2=0;
		for(ll i=p;i<p+q;++i){
			const ll mod=2*(x+y);
			if(i%mod==0){ans=min(ans,i);break;}
			ll cl=((x-i)%mod+mod)%mod,ch=p+q;
			ll g=__gcd(cl,ch);cl/=g,ch/=g;
			if(__gcd(ch,mod)!=1) continue;
			exgcd(ch,mod,pos1,pos2);pos1=(pos1%mod+mod)%mod;
			(pos1*=cl)%=mod;
			ans=min(ans,i+pos1*(p+q));
		}for(ll i=x;i<x+y;++i){
			const ll mod=p+q;
			if(i%mod==0){ans=min(ans,i);break;}
			ll cl=((p-i)%mod+mod)%mod,ch=2*(x+y);
			ll g=__gcd(cl,ch);cl/=g,ch/=g;
			if(__gcd(ch,mod)!=1) continue;
			exgcd(ch,mod,pos1,pos2);pos1=(pos1%mod+mod)%mod;
			(pos1*=cl)%=mod;
			ans=min(ans,i+pos1*2*(x+y));
		}cout<<(ans==2e18?-1ll:ans)<<endl;
	}
	return 0;
}