#include <bits/stdc++.h>
#define NM 100005
using namespace std;
ifstream fin ("lca.in");
ofstream fout ("lca.out");
int n, m, x, y, ap[NM], d[NM];
vector<int> rmq[int(log2(NM))+5];
bitset<NM> viz;
vector<int> v[NM];
void dfs(int nod)
{
    viz[nod] = 1;
    rmq[0].push_back(nod);
    ap[nod] = rmq[0].size()-1;
    for(auto it:v[nod])
        if(!viz[it])
        {
            d[it] = d[nod] + 1;
            dfs(it);
            rmq[0].push_back(nod);
        }
}
void build_rmq()
{
    int lg = rmq[0].size()-1;
    for(int i=1; i<=log2(lg);i++)
    {
        rmq[i].push_back(0);
        for(int j=1; j<=lg-(1<<i)+1; j++)
            if(d[rmq[i-1][j]] < d[rmq[i-1][j+(1<<(i-1))]])
               rmq[i].push_back(rmq[i-1][j]);
            else rmq[i].push_back(rmq[i-1][j+(1<<(i-1))]);
    }
}
void read();
int main()
{
    read();
    rmq[0].push_back(0);
    dfs(1);
    build_rmq();
    while(m--)
    {
        fin >> x >> y;
        x = ap[x], y = ap[y];
        int lg = y-x+1;
        int p = log2(lg);
        if(d[rmq[p][x]] < d[rmq[p][y-p+1]])
            fout << rmq[p][x] << '\n';
        else fout << rmq[p][y-(1<<p)+1] << '\n';
    }
    return 0;
}
void read()
{
    fin >> n >> m;
    for(int i=2; i<=n; i++)
    {
        fin >> x;
        v[x].push_back(i);
        v[i].push_back(x);
    }
}