UVa 305 - Joseph Solution

#include<iostream>
#include<list>
#include<string>
#include<cstring>
#include<sstream>
#include<cctype>
#include<string.h>
#include<algorithm>
#include<cmath>
#include<stack>
#include<fstream>
#include<cstdlib>
#include<vector>
#include<map>
#include<set>
#include<utility>
#include<iomanip>
#include<queue>

using namespace std;

#define INF (1<<29)
#define SET(a) memset(a,-1,sizeof(a))
#define ALL(a) a.begin(),a.end()
#define CLR(a) memset(a,0,sizeof(a))
#define FILL(a,v) memset(a,v,sizeof(a))
#define PB push_back
#define FOR(i,n) for(int i = 0;i<n;i++)
#define PI acos(-1.0)
#define EPS 1e-9
#define MP(a,b) make_pair(a,b)
#define min3(a,b,c) min(a,min(b,c))
#define max3(a,b,c) max(a,max(b,c))
#define READ(f) freopen(f, "r", stdin)
#define WRITE(f) freopen(f, "w", stdout)
#define LL long long
#define MX 100000
#define MOD 1000000007


int main()
{
    map<int,int>mp;
    int k,p,m,dead,newp;
    while ((cin>>k)&&k)
    {
        if(mp[k])
        {
            cout<<mp[k]<<endl;
            continue;
        }
        p = k*2;
        for(m=k; ;m++)
            {
                newp=p;
                dead=(m-1)%newp;
                while (dead>=k && newp>=k)
                {
                    newp--;
                    dead = (dead-1+m)%newp;
                }
                if (newp==k)
                    {
                        mp[k]=m;
                        break;
                    }
            }
            cout << m << endl;
        }
    }