#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#include <iostream>
#include <fstream>
#include <cmath>
#include <string>
#include <string.h>
#include <map>
#include <set>
#include <vector>
#include <algorithm>
#include <functional>
#include <list>
#include <queue>
using namespace std;

typedef long double ld;
typedef long int i64;
typedef unsigned long int u64;

const ld EPS = 1e-16;

#define sqr(a) ((a)*(a)//;

int n, k, slot = -1, leaf, mbans, poppush, m;
vector <vector <int> > a;
vector <int> dist, b, dafter[2];
queue <int> q;
vector <pair <int, int> > ans;

void dfs(int v, int ind)
{
	for (int i = 0; i < a[v].size(); ++i)
	{
		if (a[v][i] != mbans)
		{
			dfs(a[v][i], ind);
			dafter[ind][v] = max(dafter[ind][v], dafter[ind][a[v][i]] + 1);
		}
	}
}


int main()
{
	cout.precision(24);
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);

	cin >> n >> k;
	a.resize(n+5);
	b.resize(n+5);
	dist.resize(n+5);
	dafter[0].resize(n+5);
	dafter[1].resize(n+5);

	for (int i = 0; i < n; ++i)
	{
		cin >> b[i + 1];
		a[b[i + 1]].push_back(i + 1);
	}


	q.push(0);

	while (q.size())
	{
		if (a[q.front()].size() < k && slot == -1)
			slot = q.front();

		for (int i = 0; i < a[q.front()].size(); ++i)
		{
			dist[a[q.front()][i]] = dist[q.front()] + 1;
			q.push(a[q.front()][i]);
		}

		if (dist[q.front()] > dist[leaf])
			leaf = q.front();
		q.pop();
	}

	dfs(0, 0);
	int diff = dist[leaf] - dist[slot];
	ans.resize(diff);
	mbans = leaf;


	for (int i = 0; i < diff; ++i)
	{
		for (int j = 0; j < dafter[1].size(); ++j)
			dafter[1][j] = 0;
		dfs(0, 1);
		dfs(mbans, 1);
		ans[i].first = max(dafter[1][0], dist[slot] + dafter[1][mbans] + 1);
		ans[i].second = mbans;
		mbans = b[mbans];
	}


	for (int i = 0; i < ans.size(); ++i)
		if (ans[m].first > ans[i].first)
			m = i;

	cout << ans[m].second << ' ' << slot;

	return 0;
}