This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long lint;
lint dp[100];
lint a,b,p,q;
inline bool calc_valid(lint x, lint y){
    double t = log10(x)+log10(y);
    return t < 18;
}
lint f(lint x, lint y, int step){
    if(x == 0 || y == 0) return 0;
    if(x >= y){
        if(dp[step]) return dp[step];
        if(!calc_valid(q,x/y)) return dp[step] = f(y,x%y,step+1) + p;
        else return dp[step] = min(f(y,x%y,step+1) + p,f(x%y,y,step+1) + q*(x/y));
    }
    else{
        if(!calc_valid(q,y/x)) return 5e18;
        else return f(x,y%x,step+1) + q * (y/x);
    }
}
void solve(){
    memset(dp,0,sizeof(dp));
    scanf("%lld %lld %lld %lld",&a,&b,&p,&q);
    if(a < b) printf("%lld\n",min(p + f(b,a,0),f(a,b,0)));
    else printf("%lld\n",f(a,b,0));
}
int main(){
    int t;
    scanf("%d",&t);
    while (t--) {
        solve();
    }
}
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