#include <iostream>
#include <fstream>
#include <vector>
#include <cmath>
#define NMAX 500005

using namespace std;
ifstream fi("lca.in");
ofstream fo("lca.out");
int N, M;
int K = 1;

vector<int> tree[NMAX];

int visited[NMAX];

vector<pair<int, int> > sparse[20];
vector<pair<int, int> > euler;

int firstApar[NMAX];

void DFS(int node, int depth)
{
    if(visited[node])
        return;

    visited[node] = 1;

    for(auto y : tree[node])
    {
        DFS(y, depth + 1);
        euler.push_back({depth, node});
    }
}


void CreateLCASparse()
{
    euler.push_back({0, 1});

    DFS(1, 0);


    for(int i = 0; i < euler.size(); ++i)
    {
        if(firstApar[euler[i].second] == 0)
            firstApar[euler[i].second] = i;

        sparse[0].push_back(euler[i]);
    }

    K = sparse[0].size();
    cout << "BIG K: " << K << " logarithm K: " << (int) log2(K) << "\n";
    for(int i = 1; i < (int) log2(K) + 1; ++i)
        for(int j = 0; j < K - (1 << i) + 1; ++j)
            sparse[i].push_back( min(sparse[i-1][j], sparse[i-1][j + (1 << (i-1))]));
}
int main()
{
    int a, b;
    fi >> N >> M;
    for(int i = 2; i <= N; ++i)
    {
        fi >> a;
        tree[a].push_back(i);
        tree[i].push_back(a);
    }
    CreateLCASparse();

    for(int i = 1; i <= M; ++i)
    {
        fi >> a >> b;
        a = firstApar[a];
        b = firstApar[b];
        if(a > b)
            swap(a, b);
        int lq = (int) log2(b - a + 1);

        //cout <<"lq : " <<lq<<" a :" << a <<" b : " << b << " => ";
        fo << min(sparse[lq][a], sparse[lq][ b - ( 1 << lq ) + 1]).second << "\n";
        //cout << "ok\n";
    }


}