Problem:
Score : 800 points

Problem Statement

There are N towns in Snuke Kingdom, conveniently numbered 1 through N.
Town 1 is the capital.

Each town in the kingdom has a Teleporter, a facility that instantly transports a person to another place.
The destination of the Teleporter of town i is town a_i (1≤a_i≤N).
It is guaranteed that one can get to the capital from any town by using the Teleporters some number of times.

King Snuke loves the integer K.
The selfish king wants to change the destination of the Teleporters so that the following holds:

Starting from any town, one will be at the capital after using the Teleporters exactly K times in total.

Find the minimum number of the Teleporters whose destinations need to be changed in order to satisfy the king's desire.

Constraints

2≤N≤10^5

1≤a_i≤N

One can get to the capital from any town by using the Teleporters some number of times.

1≤K≤10^9

Input

The input is given from Standard Input in the following format:

N K
a_1 a_2 ... a_N

Output

Print the minimum number of the Teleporters whose destinations need to be changed in order to satisfy King Snuke's desire.

Sample Input 1

3 1
2 3 1

Sample Output 1

2

Change the destinations of the Teleporters to a = (1,1,1).

Sample Input 2

4 2
1 1 2 2

Sample Output 2

0

There is no need to change the destinations of the Teleporters, since the king's desire is already satisfied.

Sample Input 3

8 2
4 1 2 3 1 2 3 4

Sample Output 3

3

For example, change the destinations of the Teleporters to a = (1,1,2,1,1,2,2,4).

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <vector>
#include <iterator>
#include <map>
#include <cstdio>
#include <functional>
#include <array>
template<typename T> struct ScanfSpecifier{};
#define DEF(T,V) template<> struct ScanfSpecifier<T>{static constexpr const char* value = V;};
DEF(int,"%d")DEF(double,"%lf")DEF(float,"%f")DEF(char,"%c")DEF(const char*,"%s")DEF(unsigned long,"%lu")DEF(unsigned int, "%u")
#ifdef _MSC_VER
DEF(long long int,"%I64d")
#else
DEF(long long int,"%lld")
#endif
#undef DEF
template<typename T> int RD(T& arg){return std::scanf(ScanfSpecifier<T>::value, &arg);}
template<int S> int RD(char (&arg)[S]){return std::scanf("%s", arg);}
int RD(char* arg){return std::scanf("%s", arg);}
template<> int RD<char>(char& arg){return std::scanf(" %c", &arg);}
template<typename T, typename... Args> int RD(T& arg1, Args&... args) {return RD(arg1) + RD(args...);}
template<typename T> T RD(){T ret; RD(ret); return ret;}
template<typename It> void RDV(It begin, It end) { while(begin != end) RD(*begin++); }
template<typename C> void RDV(C& c) {RDV(std::begin(c), std::end(c));}
template<typename... Args> void WT(Args... args) { int alc = 0; int dummy[] = {((alc++? std::printf(" "): 0), std::printf(ScanfSpecifier<Args>::value, args), 0)...}; }
template<typename... Args> void WTL(Args... args) { WT(args...); std::printf("\n"); }
template<typename It> void WTV(It begin, It end) { int alc = 0; while(begin != end) (alc++? std::printf(" "): 0), WT(*begin++); }
template<typename C> void WTV(const C& c) {WTV(std::begin(c), std::end(c));}
template<typename It> void WTVL(It begin, It end) { WTV(begin, end); std::printf("\n"); }
template<typename C> void WTVL(const C& c) {WTVL(std::begin(c), std::end(c));}



namespace XX
{   
    template<template<typename> class Compare, typename T>
    inline T& UP(T& x, const T& y){if(Compare<T>()(y, x)) x = y; return x;}
    template<typename Compare, typename T>
    inline T& UP(T& x, const T& y, Compare comp){if(comp(y, x)) x = y; return x;}

    template<typename T> inline T& GT(T& x, const T& y){return UP<std::greater>(x, y);}
    template<typename T> inline T& LS(T& x, const T& y){return UP<std::less>(x, y);}

    template<typename T>
    struct Mapper
    {
        int operator[](const T& v) { int& ret = table[v]; if(!ret) rtable[ret = table.size()] = v; return ret - 1; }
        template<typename... Args> int operator()(Args... args) { return (*this)[T(args...)]; }
        T rev(int idx){return rtable[idx + 1];}
        std::map<T, int> table;
        std::map<int, T> rtable;
    };

    template<typename T, int S>
    struct ReferenceArray
    {
        struct It {typename std::array<T*, S>::iterator it; T& operator*(){return **it;} void operator++(){it++;} bool operator!=(const It& other){return it != other.it;} };
        int size()const{return _ptr.size();}
        It begin()const{return {_ptr.begin()};}
        It end()const{return {_ptr.end()};}
        T& operator[](int idx)const{return *_ptr[idx];}
        mutable std::array<T*, S> _ptr;
    };
    template<typename T, typename... Args> 
    ReferenceArray<T, sizeof...(Args) + 1> MAKEV(T& arg1, Args&... args) {return {&arg1, &args...};}

    struct Range
    {   
        struct It {   int num, step; int operator*(){return num;} void operator++(){num += step;} bool operator!=(const It& other){return num != other.num;} };
        Range(int ee):b(0),e(ee){}
        Range(int bb, int ee):b(bb), e(ee){}
        It begin(){return {b, (b < e? 1: -1)};}
        It end(){return {e, 0};}
        int b, e;
    };

}





//alias
template<typename T> T& UMAX(T& x, T y){return XX::UP<std::greater>(x, y);}
template<typename T> T& UMIN(T& x, T y){return XX::UP<std::less>(x, y);}
using XX::UP; //(x,y) comp
using RG = XX::Range;
using XX::MAKEV;
using XX::Mapper;
//RD[L],RDV[L],WT[L],WTV[L] for i/o
//template
#include <vector>
#include <string>
#include <set>
#include <map>
#include <cstdlib>
#include <algorithm>
#include <functional>
using namespace std;

vector<int> adj[100009];

int A[100009];
int ans;
int N, K;
int dfs(int u)
{
    int deep = 0;
    for(int to: adj[u])
    {
        int res = dfs(to);
        if(res < K)
            UMAX(deep, res);
        else if(u != 1)
            ans++;
    }
    return deep + 1;
}

int main()
{
    RD(N, K);
    RDV(A + 1, A + N + 1);

    for(int i = 2; i <= N; i++)
        adj[A[i]].push_back(i);

    ans = A[1] != 1;

    dfs(1);

    WTL(ans);

}