#include <bits/stdc++.h>

using namespace std;
ifstream fin("lca.in");
ofstream fout("lca.out");
int tat[100001],N,M;
int lg[100001],rmq[20][100001],rmqcop[20][100001];

vector <int> ad[100001],elem,grad;

int poz[100001];

void read()
{fin>>N>>M;

 for(int i=2;i<=N;i++)
        {fin>>tat[i];
         ad[tat[i]].push_back(i);
        }
}

void dfs(int nod,int grade)
{elem.push_back(nod);
 grad.push_back(grade);
 for(int i = 0 ; i < ad[nod].size() ; i++)
    {
     dfs(ad[nod][i],grade+1);

     elem.push_back(nod);

     grad.push_back(grade);
    }
}

void RMQ()
{    int x,y;
     for(int i=0;i<elem.size();i++)
        {
         rmq[0][i]=grad[i];
         rmqcop[0][i]=elem[i];
        }
    lg[2]=1;
    for(int i=3;i<=100001-2;++i)
        lg[i]=lg[i/2]+1;

    for(int i=1; ( 1 << i) <= elem.size(); ++i)

        for(int j=1; j + ( 1 << i ) - 1 <= elem.size(); ++j)
        {
            rmq[i][j] = min ( rmq[i-1][j] , rmq[i-1][j + ( 1 << (i-1) )]);
            if ( rmq[i-1][j] < rmq[i-1][j + ( 1 << (i-1) ) ] )
                rmqcop[i][j] = rmqcop[i-1][j];
            else
                rmqcop[i][j] = rmqcop[i-1][j + ( 1 << (i-1) ) ];
        }
    for(int i = 1; i <= M; ++i)
    {
        fin >> x >> y;
        if(poz[y]<poz[x])swap(x,y);
        int L=(poz[y]-poz[x])+1;
        if(rmq[lg[L]][poz[x]] < rmq[lg[L]][poz[y] - ( 1 << lg[L] ) + 1])
            fout << rmqcop[lg[L]][poz[x]]<<"\n";
        else
            fout<<rmqcop [lg[L]][poz[y] - ( 1 << lg[L] ) + 1]<<"\n";


        //fout << min(rmq[lg[L]][poz[x]], rmq[lg[L]][poz[y] - ( 1 << lg[L] ) + 1])<<"\n";
    }
}

void Do()
{int i;
 for(i=0 ; i <= elem.size() ; i++)
    if(poz[ elem[i] ] == 0)
        {
         poz[ elem [i] ] = i;
        }
 RMQ();


}
int main()
{
    read();
    dfs(1,1);
    Do();
    //for(int i=0;i<elem.size();i++)
        //cout<<grad[i]<<" ";
    return 0;
}