#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
double C(int n, int k)
{
k = min(n-k, k);
double t = 1;
for(int i=1; i<=k; ++i)
t = t * (n-i+1) / i;
return t;
}
class EagleInZoo { public:
double calc(vector <int> parent, int K)
{
int N = parent.size() + 1;
vector<vector<int>> child(N);
for(int i=1; i<N; ++i)
child[parent[i-1]].push_back(i);
return rec(child, 0, K);
}
map<pair<int,int>,double> memo;
double rec(const vector<vector<int>>& child, int v, int K)
{
if(K == 1)
return 1.0;
if(child[v].empty())
return 0.0;
pair<int,int> key(v, K);
if(memo.count(key)) return memo[key];
double ans = 0.0;
for(int u: child[v]) // When K-the eagle goes to |u|.
for(int uN=0; uN<=K-2; ++uN) // When uN out of K-2 previous eagles went to |u|.
{
ans += C(K-2, uN)
* pow(1.0/child[v].size(), uN)
* pow(1.0-1.0/child[v].size(), K-2-uN)
* rec(child, u, uN+1);
}
return memo[key] = ans / child[v].size();
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const double& Expected, const double& Received) {
bool ok = (abs(Expected - Received) < 1e-9);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, EagleInZoo().calc(parent, K));}
int main(){
CASE(0)
int parent_[] = {0,0};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int K = 2;
double _ = 1.0;
END
CASE(1)
int parent_[] = {0,0};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int K = 3;
double _ = 0.5;
END
CASE(2)
int parent_[] = {0,1,0,3};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int K = 4;
double _ = 0.75;
END
CASE(3)
int parent_[] = {0,0,1,1,2,4,4,4,5,5,6,6};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int K = 20;
double _ = 0.14595168754091617;
END
CASE(4)
int parent_[] = {0,1,2,3,2,1,1,7,0,9,10,11,12,13,14,15,16,17,18,14,9};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int K = 24;
double _ = 0.3272154791654077;
END
CASE(5)
int parent_[] = {0,1,2,3,4,5,6,7,8,9,10};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int K = 50;
double _ = 0.0;
END
/*
CASE(6)
int parent_[] = ;
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int K = ;
double _ = ;
END
CASE(7)
int parent_[] = ;
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int K = ;
double _ = ;
END
*/
}
// END CUT HERE