#include <bits/stdc++.h>
#define NMAX 100001
using namespace std;

ifstream fin("lca.in");
ofstream fout("lca.out");

int N, M;
vector<vector<int>> tree(NMAX, vector<int>());

vector<int> euler_tour(1, 0);

int first_appearance[NMAX], old_index[NMAX];

int id = 1;

void DFS(int node, int parent)
{
    int new_index = id;

    ++id;

    euler_tour.push_back(new_index);

    old_index[new_index] = node;

    first_appearance[node] = euler_tour.size() - 1;

    for(auto& next : tree[node])
    {
        if(next != parent)
        {
            DFS(next, node);
            euler_tour.push_back(new_index);
        }
    }
}

vector<vector<int>> dp(2*NMAX, vector<int>(20));
vector<size_t> lg(2*NMAX, 0);

int main()
{
    fin >> N >> M;

    for(int x, i = 1; i <= N - 1; ++i)
        fin >> x,
        tree[x].push_back(i + 1),
        tree[i + 1].push_back(x);

    DFS(1, 0);

    size_t P = euler_tour.size() - 1;

    for(size_t i = 2; i <= P; ++i)
        lg[i] = lg[i >> 1] + 1;

    for(size_t i = 1; i <= P; ++i)
        dp[i][0] = euler_tour[i];


    for(size_t i = 1; i <= lg[P]; ++i)
        for(size_t j = 1; j - 1 + (1 << i) <= P; ++j)
            dp[j][i] = min(dp[j][i - 1], dp[j + (1 << (i - 1))][i - 1]);


    for(int x, y, f1, f2, k, i = 1; i <= M; ++i)
    {
        fin >> x >> y;
        f1 = first_appearance[x];
        f2 = first_appearance[y];

        if(f1 > f2) swap(f1, f2);

        k = lg[f2 - f1 + 1];

        fout << old_index[min(dp[f1][k], dp[f2 + 1 - (1 << k)][k])] << '\n';

        if(old_index[min(dp[f1][k], dp[f2 + 1 - (1 << k)][k])] == -1)
        {
            cout << f1 << " " << f2 << endl;
        }
    }

}