Get there faster

#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;

/// Compiles just fine (TM) with G++ 4.7 in -std=c++0x mode

typedef unsigned __int128 llu;
typedef long long unsigned ull;

llu bb(llu x){
  llu best=x;
  if (x==1) return 1;
  llu k=1,kb=2;
  while (kb<=x){
    llu l=k,r=(__int128)-1; r>>=(__int128)2;
    while (l<r){
      llu n=(l>>(__int128)1)+(r>>(__int128)1)+(l&r&1);
      llu res=1;
      for (llu m=1; m<=k and res<=x; m++)
        res*=(m+n-k),res/=m;
      if (res==x){
        best=min(best,n);
        break;
      }
      if (res<x) l=n+1;
      else r=n;
    }
    ++k;kb*=(k*2-1)*(k*2),kb/=k*k;
  }
  return best;
}

int main(){
  if(freopen("checkpoint.in","r",stdin));
  if(freopen("checkpoint.out","w",stdout));

  int tsts; if(scanf("%d",&tsts)); for (int tst=1; tst<=tsts; tst++){
    llu ways; ull proxy; if(scanf("%llu",&proxy)); ways=proxy;
    llu best=-1;
    for (llu i=1; i*i<=ways; i++)
      if (ways%i==0)
        best=min(best,bb(i)+bb(ways/i));
    printf("Case #%d: %llu\n",tst,(ull)best);
  }
}