#include<stdio.h>
#include<vector>
using namespace std;
int nr, niv,euler[100004<<1],nivel[100004<<1],f[100004<<1],lg[100004<<1];
vector<int> v[100004];
int dfs(int k,int niv)
{

    nr++;
    euler[nr]=k;
    nivel[nr]=niv;
    if(f[k]==0)
        f[k]=nr;
    for(int i=0;i<v[k].size();i++)
    {


        dfs(v[k][i],niv+1);

        nr++;
        euler[nr]=k;
        nivel[nr]=niv;

    }
}
int rmq[100004<<1][30],sol[100004<<1][30];
int n,m,x;
int main()
{
    int i;
    freopen("lca.in","r",stdin);
    freopen("lca.out","w",stdout);
    scanf("%d%d",&n,&m);
    for(i=1;i<=n-1;i++)
    {

        scanf("%d",&x);
        v[x].push_back(i+1);
    }
    dfs(1,0);
   /*for(i=1;i<=nr;i++)
        printf("%d ",euler[i]);
    printf("\n");
    for(i=1;i<=nr;i++)
        printf("%d ",nivel[i]);
   printf("\n");*/

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

    for(i=1;i<=nr;i++)
    {

        rmq[i][0]=nivel[i];
        sol[i][0]=euler[i];
    }
    for(int j=1;(1<<j)<=nr;j++)
    {

        for(int i=1;i<=nr-(1<<j);i++)
        {
            int l=1<<(j-1);
            if(rmq[i][j-1]>rmq[i+l][j-1])
            {
                rmq[i][j]=rmq[i+l][j-1];
                sol[i][j]=sol[i+l][j-1];

            }
            else
            {
                rmq[i][j]=rmq[i][j-1];
                sol[i][j]=sol[i][j-1];
            }

        }

    }
    int y;
 /*   for(i=1;i<=n;i++)
        printf("%d ",f[i]);
    printf("\n");*/
    for(i=1;i<=m;i++)
    {
        scanf("%d%d",&x,&y);

        x=f[x];
        y=f[y];
        if(x>y)
            swap(x,y);
       // printf("%d %d\n",x,y);
        int diff=y-x+1;
        int l=lg[diff];
        if(rmq[x][l]>rmq[y-(1<<(l))+1][l])        {

            printf("%d\n",sol[y-(1<<(l))+1][l]);
        }
        else printf("%d\n",sol[x][l]);

        }

        return 0;
    }