josephus o(n).cpp

#include<bits/stdc++.h>

#define       PI                        acos(-1)
#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       lli                         long long int
#define       ull                        unsigned long long int
#define       pii                       pair < int, int>
#define       pll                        pair < ll, ll>
#define       sc                       scanf
#define       scin(x)                sc("%d",&(x))
#define       scln(x)                sc("%lld",&(x))
#define       pf                        printf
#define       veci                    vector<int>
#define       vecl                    vector<long long int>
#define       vecp                   vector<  pair<int,int> >
#define       pb                      push_back
#define       inf                      1<<30
#define       mp                     make_pair
#define       ss                      stringstream
#define       all(v)                  v.begin(), v.end()
#define       mem(x,y)          memset(x,y,sizeof(x))
#define       FastRead         ios_base::sync_with_stdio(0);cin.tie(0)
#define       M                      1000000007
//int month[]={31,28,31,30,31,30,31,31,30,31,30,31};
//long power(long int x, long int y){ int temp; if( y == 0) return 1; temp = power(x, y/2); if (y%2 == 0) return temp*temp; else return x*temp*temp; }
/*lli gcd(lli x,lli y)
{
    if(x==0) return y;
    return gcd(y%x,x);
}*/
using namespace std;
int j ( int n , int k )
{
    if(n==1 )  return 1;
    return  ( j(n - 1 , k ) + k-1 ) % n + 1 ;
}

int main()
{
    int n , k ;
    cin >> n >> k ;

    cout << "The last person to stay alive is at position : " << j ( n , k ) << endl;


    return 0;
}