#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;
class WalkOverATree { public:
int maxNodesVisited(vector <int> parent, int L)
{
const int N = parent.size() + 1;
vector<vector<int>> G(N);
for(int i=0; i<parent.size(); ++i)
G[parent[i]].push_back(i+1);
vector<int> numBelow(N); {
function<int(int)> rec;
rec = [&](int v) {
int cnt = 1;
for(auto u: G[v])
cnt += rec(u);
return numBelow[v] = cnt;
};
rec(0);
}
function<int(int, int)> rec;
map<pair<int,int>, int> memo;
rec = [&](int v, int L) {
const pair<int,int> key(v, L);
if(memo.count(key)) return memo[key];
const vector<int>& child = G[v];
if(L<=0 || child.empty())
return 1;
int visMax = 0;
for(int i=0; i<child.size(); ++i) {
set<int> previsit;
previsit.insert(0);
for(int k=0; k<child.size(); ++k) if(i!=k) {
set<int> pv2 = previsit;
for(int z: previsit)
pv2.insert(z + numBelow[child[k]]);
previsit = pv2;
}
for(int p: previsit) if(p*2 <= L)
visMax = max(visMax, 1 + p + rec(child[i], L-p*2-1));
}
return memo[key] = visMax;
};
return rec(0, L);
}
};
// 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 int& Expected, const int& Received) {
bool ok = (Expected == Received);
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(_, WalkOverATree().maxNodesVisited(parent, L));}
int main(){
/*
CASE(0)
int parent_[] = {0, 0};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 2;
int _ = 2;
END
*/
CASE(1)
int parent_[] = {0, 0};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 3;
int _ = 3;
END
CASE(2)
int parent_[] = {0, 1, 2, 3};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 2;
int _ = 3;
END
CASE(3)
int parent_[] = {0,0,0,0,2,4,2,3,1};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 1;
int _ = 2;
END
CASE(4)
int parent_[] = {0,0,1,2,3,2,3,1,3,0,1,8,6,8,0,5,15,0,9};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 4;
int _ = 5;
END
CASE(5)
int parent_[] = {0,0,0,1,1,3,5,1,4,5,2,2,10,5,10,10,11,13,8,3,18,15,20,20,23,8,11,26,4};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 26;
int _ = 17;
END
CASE(6)
int parent_[] = {0, 0, 2, 0}
;
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 100;
int _ = 5;
END
CASE(7)
int parent_[] = {0, 0, 2};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 4;
int _ = 4;
END
CASE(8)
int parent_[] = {0,1,2,0,4,4,4,4};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 3;
int _ = 4;
END
CASE(9)
int parent_[] = {0,0,2,0,4,5};
vector <int> parent(parent_, parent_+sizeof(parent_)/sizeof(*parent_));
int L = 7;
int _ = 6;
END
}
// END CUT HERE