#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
using namespace std;
typedef long long LL;

class ShufflingMachine
{
public:
	double stackDeck(vector <int> shuffle, int maxShuffles, vector <int> cardsReceived, int K) 
	{
		set<int> my( cardsReceived.begin(), cardsReceived.end() );

		vector<int> cur(shuffle.size());
		for(int i=0; i<cur.size(); ++i)
			cur[i] = i;

		vector<double> prob(shuffle.size());
		for(int N=1; N<=maxShuffles; ++N)
		{
			for(int i=0; i<cur.size(); ++i)
				cur[i] = shuffle[cur[i]];

			for(int i=0; i<cur.size(); ++i)
				if( my.count(cur[i]) )
					prob[i] += 1.0 / maxShuffles;
		}

		sort( prob.rbegin(), prob.rend() );
		return accumulate( prob.begin(), prob.begin()+K, 0.0 );
	}

// BEGIN CUT HERE
	public:
	void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); if ((Case == -1) || (Case == 4)) test_case_4(); }
	private:
	template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
	void verify_case(int Case, const double &Expected, const double &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } }
	void test_case_0() { int Arr0[] = {1,0}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 3; int Arr2[] = {0}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 1; double Arg4 = 0.6666666666666666; verify_case(0, Arg4, stackDeck(Arg0, Arg1, Arg2, Arg3)); }
	void test_case_1() { int Arr0[] = {1,2,0}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 5; int Arr2[] = {0}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 2; double Arg4 = 0.8; verify_case(1, Arg4, stackDeck(Arg0, Arg1, Arg2, Arg3)); }
	void test_case_2() { int Arr0[] = {1,2,0,4,3}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 7; int Arr2[] = {0,3}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 2; double Arg4 = 1.0; verify_case(2, Arg4, stackDeck(Arg0, Arg1, Arg2, Arg3)); }
	void test_case_3() { int Arr0[] = {0,4,3,5,2,6,1}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 19; int Arr2[] = {1,3,5}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 2; double Arg4 = 1.0526315789473684; verify_case(3, Arg4, stackDeck(Arg0, Arg1, Arg2, Arg3)); }
	void test_case_4() { int Arr0[] = {3,4,7,2,8,5,6,1,0,9}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 47; int Arr2[] = {6,3,5,2,8,7,4}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 8; double Arg4 = 6.297872340425532; verify_case(4, Arg4, stackDeck(Arg0, Arg1, Arg2, Arg3)); }

// END CUT HERE
};
// BEGIN CUT HERE 
int main() {
	ShufflingMachine().run_test(-1);
}
// END CUT HERE
