#include <fstream>
#include <vector>

using namespace std;

ifstream fin( "lca.in" );
ofstream fout( "lca.out" );

const int NMAX = 500005;
const int KMAX = 22;

int N, nr_q;

vector <int> Ad[NMAX];

int pos[NMAX];
int euler[2 * NMAX];
int lvl[NMAX];
int last;

int lg[2 * NMAX];

int mat[KMAX][NMAX];


void Read()
{
  fin >> N >> nr_q;

  int x;
  for( int i = 2; i <= N; ++i )
  {
    fin >> x;

    Ad[x].push_back( i );
  }
}

void DFS( int nod, int depth )
{
  euler[++last] = nod;

  if( pos[nod] == 0 )
  {
    pos[nod] = last;
    lvl[nod] = depth;
  }

  for( int i = 0; i < Ad[nod].size(); ++i )
  {
    DFS( Ad[nod][i], depth + 1 );

    euler[++last] = nod;
    //lvl[last] = nod;
  }
}

void Do()
{
  DFS( 1, 1 );

  for( int i = 2; i <= last; ++i )
    lg[i] = lg[i / 2] + 1;

  for( int i = 1; i <= last; ++i )
    mat[0][i] = euler[i];

  int aux;

  for( int i = 1; ( 1 << i ) <= last; ++i )
    for( int j = 1; j + ( 1 << i ) - 1 <= last; ++j )
    {
      mat[i][j] = mat[i - 1][j];

      aux = j + ( 1 << ( i - 1 ) );

      if( lvl[ mat[i - 1][j] ] > lvl[ mat[i - 1][aux] ] )
        mat[i][j] = mat[i - 1][aux];
    }

 /*
  for( int i = 0; ( 1 << i ) < last; ++i )
  {
    for( int j = 1; j <= last; ++j )
      fout << mat[i][j] << ' ';
{1}
    fout << '\n';
  }*/

  int x, y;
  int logg, ans;

  for( int i = 1; i <= nr_q; ++i )
  {
    fin >> x >> y;

    x = pos[x]; y = pos[y];

    if( x > y ) swap( x, y );

    logg = lg[y - x + 1];
    aux = y - ( 1 << logg ) + 1;

    ans = mat[logg][x];

    //fout << ans << ' ' << mat[logg][aux] << '\n';

    if( lvl[ans] > lvl[ mat[logg][aux] ] )
     ans = mat[logg][aux];

    fout << ans << '\n';
  }
}

int main()
{
    Read();
    Do();

    return 0;
}