#include <iostream>
#include <fstream>
using namespace std;
ifstream f("lca.in");
ofstream g("lca.out");
int n, v[100500], m, nivel[200500], t[300000], j=1, nr, viz[100500], prima[100050];
int rmq[50][200000],lg[200000], M;
void citire()
{
    f>>n>>m;
    int i;v[0]=1;
    for(i=1;i<n;++i)
        f>>v[i];
}
void niv (int nod)
{
    if(nod==1 && v[nod]==1)  nivel[nod]=0;
    else
        nivel[nod]=nivel[v[nod-1]]+1;
}
void dfs(int x)
{
    int i;
    t[++M]=x;
    viz[x]=1;
    for(i=x+1;i<=n;++i)
        if(!viz[i] && v[i-1]==x)
        {
            dfs(i);
            t[++M]=x;
        }
}
void rmq1 (int N[])
{
    int i, k, l;
    for (i=2;i<=M;++i)
        lg[i]=lg[i/2]+1;
    for (i=1;i<=M;++i)
        rmq[0][i]=N[i];
    for (i=1;(1<<i)<=M;++i)
       for (k=1;k<=M-(1<<i)+1;++k)
        {
            l=1<<(i-1);
            rmq[i][k]= min(rmq[i-1][k],rmq[i-1][k+l]);
        }
}
int main()
{
    citire();
    int i, diff,l, sh ;
    for(i=1;i<=n;++i)
        niv(i);
    dfs(1);
    M--;
    int N[M+1];
    for(i=1;i<=M;++i)
    {
        N[i]=nivel[t[i]];
        if(prima[t[i]]==0)  prima[t[i]]=i;
    }
    rmq1(N);
    while(m--)
    {
        int x, y, mi, ok=0;
        f>>x>>y;
        x=prima[x]; y=prima[y];
        if(x>y)
            {
                x=x^y;
                y=x^y;
                x=x^y;
            }
        diff=y-x+1;
        l=lg[diff];
        sh=diff-(1<<l);
        mi=min(rmq[l][x],rmq[l][x+sh]);
        for(i=x;i<=y && ok==0;++i)
            if(N[i]==mi)
                ok=1, g<<t[i]<<"\n";
    }

    g.close();
}