UVA 10940 Throwing cards away II

#include <map>
#include <set>
#include <list>
#include <cmath>
#include <ctime>
#include <deque>
#include <stack>
#include <queue>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#define LL long long
#define PI 3.1415926535897932626
using namespace std;
int gcd(int a, int b) {return a % b == 0 ? b : gcd(b, a % b);}
#define MAXN 500003
vector<int>tab[20];
int num[20];
int N;
void init()
{
    for (int i=0;i<20;i++) tab[i].clear();
    tab[0].push_back(1);
    for (int i=1;i<20;i++)
    {
        int limit=1<<i;
        int cas=2;
        while (cas<=limit)
        {
            tab[i].push_back(cas);
            cas+=2;
        }
    }
    num[0]=1;
    for (int i=1;i<20;i++) num[i]=num[i-1]+tab[i].size();
}
int main()
{
    init();
    while (scanf("%d",&N)!=EOF)
    {
        if (N==0) break;
        if (N==1) {puts("1");continue;}
        int cas=0,i;
        for ( i=0;i<20;i++)
        {
            cas+=tab[i].size();
            if (cas>=N) break;
        }
        int tmp=N-num[i-1];
        printf("%d\n",tab[i][tmp-1]);
    }
    return 0;
}