UVA 10077 C++

#include<iostream>
#include<string>
using namespace std;
int main()
{
START:
string path="";
int m,n;
while(cin>>m,cin>>n)
{
if( m==1 && n==1)
break;
int uppertop=1,upperdown=0,lowertop=0,lowerdown=1;
int midtop,middown;
double mid,mn;
while(true)
{
midtop=uppertop+lowertop;
middown=upperdown+lowerdown;
mid=midtop*1.0/middown;
mn=m*1.0/n;
if(midtop==m && middown==n)
{
cout<<path<<endl;
goto START;
}
else if(mid>=mn)
{
uppertop=midtop;
upperdown=middown;
path=path+'L';
}
else
{
lowertop=midtop;
lowerdown=middown;
path=path+'R';
}
}

}
return 0;
}