#include <algorithm>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <vector>
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
// Debug printing
#ifdef DEBUG
#define deb(fmt, args...) printf("DEBUG: %d: " fmt, __LINE__, ##args)
#else
#define deb(fmt, args...)
#endif
void print_pair_ar(vector<pair<int, int>> in, const string title = "Vector")
{
cout << title << " [\n";
for (unsigned int i = 0; i < in.size(); i++) {
pair el = in[i];
cout << "row " << i << ": " << "{" << el.first << ", " << el.second << "} \n";
}
cout << "\n] END\n";
}
void print_array(vector<int> in, const string title = "Vector")
{
cout << title << " [\n";
for (const auto &el : in) {
cout << el << " ";
}
cout << "\n] END\n";
}
void print_matrix(vector<vector<int> > in, const string title = "Matrix")
{
cout << title << " [\n";
for (unsigned int i = 0; i < in.size(); i++) {
cout << "row " << i << ": ";
for (unsigned int j = 0; j < in[i].size(); j++) {
cout << in[i][j] << " ";
}
cout << "\n";
}
cout << "] END\n";
}
void dfs(int s, vector<bool> &visited, vector<vector<int> > &adj,
vector<pair<int, int> > &traversal, int depth)
{
if (visited[s]) {
return;
};
visited[s] = true;
traversal.push_back({ s, depth });
for (auto u : adj[s]) {
dfs(u, visited, adj, traversal, depth + 1);
traversal.push_back({ s, depth });
}
}
void build_sparse_table(vector<pair<int, int> > &in,
vector<vector<pair<int, int> > > &sparse)
{
int rows = 1;
rows = log2(in.size()) + 1;
sparse.clear(); // clear table
sparse.push_back(vector<pair<int, int> >());
for (unsigned int i = 0; i < in.size(); i++) {
sparse[0].push_back(in[i]);
}
for (int i = 1; i < rows; i++) {
sparse.push_back(vector<pair<int, int> >()); // needed rows
int len = 1 << i;
int w = len / 2;
for (unsigned int j = 0; j < in.size() - len + 1; j++) {
pair<int, int> minimum =
sparse[i - 1][j].second <
sparse[i - 1][j + w].second ?
sparse[i - 1][j] :
sparse[i - 1][j + w];
// int minimum =
// min(sparse[i - 1][j], sparse[i - 1][j + w]);
sparse[i].push_back(minimum);
}
}
}
int query_sparse_table(int a, int b, vector<vector<pair<int, int> > > &sparse)
{
int L = min(a, b);
int R = max(a, b);
// deb("L: %d, R: %d\n", L, R);
int num = 1;
if (L == R) {
if (L == 0)
return 1;
return sparse[0][L - 1].first;
}
while (num < R - L)
num <<= 1;
if (num != R - L) {
num >>= 1;
}
int row = log2(num);
int el = sparse[row][L].second < sparse[row][R - num].second ?
sparse[row][L].first :
sparse[row][R - num].first;
return el;
// return min(sparse[row][L].first, sparse[row][R - num].first);
}
int main(int argc, char *argv[])
{
// Read the input parameters
int n, q;
cin >> n >> q;
// Read values from one line
vector<vector<int> > kids(n + 1, vector<int>());
int tmp;
for (int i = 0; i < n - 1; i++) {
cin >> tmp;
kids[tmp].push_back(i + 2);
}
// print_matrix(kids);
// Build traversal array
vector<bool> visited(n, false);
vector<pair<int, int> > traversal;
dfs(1, visited, kids, traversal, 1);
// Find the first occurence of node
vector<int> first(n + 1, -1);
for (unsigned int i = 0; i < traversal.size(); i++) {
if (first[traversal[i].first] == -1) {
first[traversal[i].first] = i;
}
// deb("i: %d, traversal[i]: %d, first[traversal[i]]: %d\n", i,
// traversal[i], first[traversal[i]]);
}
// first[0] = 0;
// print_pair_ar(traversal, "traversal");
// print_array(first, "first");
// Build sparse table
vector<vector<pair<int, int> > > sparse;
build_sparse_table(traversal, sparse);
// for (unsigned int i = 0; i < sparse.size(); i++) {
// print_pair_ar(sparse[i]);
// }
// print_matrix(sparse);
// Do queries
int l, r;
for (int i = 0; i < q; i++) {
cin >> l >> r;
// deb("l: %d, r: %d\n", l, r);
l = max(first[l] - 1, 0);
// l = first[l];
r = first[r];
// deb("väli (%d, %d)\n", l, r);
int res = query_sparse_table(l, r, sparse);
cout << res << "\n";
}
return 0;
}