#include <fstream>
#define MaxN 100528
#define MaxL 100

using namespace std;

fstream fin ("lca.in",ios::in);
fstream fout("lca.out",ios::out);

struct nod {
	int x;
	nod *urm;
};

int n, m, viz[MaxN], k, parc[MaxN<<2], dep[MaxN<<2];
nod *L[MaxN];
int first[MaxN], Lg[MaxN<<2 + 3], M[MaxL][MaxN];

void rmq(){
	for(int i = 2; i <= k; ++i)
		Lg[i] = Lg[i >> 1] + 1;
	for(int i = 1; i <= k; ++i)
		M[0][i] = i;

	for(int i = 1; (1 << i) < k; ++i)
		for(int j = 1; j <= k - (1 << i); ++j)
		{
			int l = 1 << (i - 1);
			M[i][j] = M[i-1][j];
			if(dep[M[i-1][j + l]] < dep[M[i][j]])
				M[i][j] = M[i-1][j + l];
}
	
};

void add_nod(int ex1, int ex2){

	nod *p = new nod;
	nod *q = new nod;

	p->x = ex2;
	p->urm = L[ex1];
	L[ex1] = p;

	q->x = ex1;
	q->urm = L[ex2];
	L[ex2] = q;
};

void euler_det(int x, int depth){ //dfs euler

		viz[x] = 1;
		parc[++k] = x;
		dep[k] = depth;
		first[x] = k;
		for (nod *p = L[x]; p != NULL; p = p->urm)
			if (!viz[p->x]){
				euler_det(p->x, depth + 1);
				parc[++k] = x;
				dep[k] = depth;

			};
};

int query(int x1, int x2){
	
	if (x1 > x2){
		int aux;
		aux = x1;
		x1 = x2;
		x2 = x1;
	};
	
	int dif = x2 - x1 + 1;
	int l = Lg[dif];
	
	if (dep[M[l][x1]] <= M[l][x2 - (1 << l) + 1])
		return M[l][x1];
	return M[l][x2 - (1 << l) + 1];
};

int main(){
	
	int x, x1, x2;
	
	fin>>n>>m;
	for (int i = 2; i <= n; ++i){
		fin>>x;
		add_nod(i, x);
	};

	euler_det(1, 0);

	//preprocesarea RMQ	
	Lg[1] = 0;
	for (int i = 2; i <= k; i++)
		Lg[i] = Lg[i >> 1] + 1;
	rmq();

	//efectuarea query-urilor
	/*for (int i = 1; i <= k; ++i)
		fout<<parc[i]<<' ';
	fout<<'\n';
	for (int i = 1; i <= k; ++i)
		fout<<first[i]<<' ';
	fout<<'\n';*/
	for (int i = 1; i <= m; ++i){
		fin>>x1>>x2;
		fout<<parc[query(first[x1], first[x2]) -1 ]<<' '<<dep[query(first[x1], first[x2])]<<'\n';
	};
	
	return 0;
};