#include <bits/stdc++.h>
using namespace std;

int T,l,m,size;
int la,lb,ma,mb;

int main() {
    
    cin >> T;
    while(T--){
        cin >> la >> lb >> ma >> mb;
        
        l = la + lb;
        
        if(la <= ma && lb <= mb){
            cout << l << endl;
        }
        else if(la > ma && lb > mb){
            if(abs(la*1.0/ma-lb*1.0/mb) <= 1) cout << l << endl;
            else cout << (la*1.0/ma>lb*1.0/mb ? la+(la+1)*mb : lb+(lb+1)*ma) << endl;
        }
        else if(la <= ma) cout << min(la+(la+1)*mb,l) << endl;
        else if(lb <= mb) cout << min(lb+(lb+1)*ma,l) << endl;
    }
    
    return 0;
}