#include <fstream>
#include <vector>
using namespace std;
ifstream fin ("lca.in");
ofstream fout("lca.out");
int n,m,i,k,x,y,j,l,t,viz[100001],P[400001];
vector <int> V[100001];
struct elem
{
    int e,h;
}E[400001],D[20][400001];
void dfs(int x,int h)
{
    viz[x]=1;
    E[++k]={x,h};
    for(int j=0;j<V[x].size();j++)
    {
        int vecin=V[x][j];
        if(!viz[vecin])
        {
            dfs(vecin,h+1);
            E[++k]={x,h};
        }
    }
}
elem minim(elem x,elem y)
{
    if(x.h>y.h)
    {
        elem z=y;
        return z;
    }
    else
    {
        elem z=x;
        return z;
    }
}
int main()
{
    fin>>n>>m;
    for(i=2;i<=n;i++)
    {
        fin>>t;
        V[t].push_back(i);
        V[i].push_back(t);
    }
    dfs(1,0);
    for(i=1;i<=k;i++)
        D[0][i]={i,E[i].h};
    for(l=1;(1<<l)<=k;l++)
    {
        for(i=1;i<=k;i++)
        {
            D[l][i]=D[l-1][i];
            j=i+(1<<(l-1));
            if(j<=k&&D[l][i].h>D[l-1][j].h)
                D[l][i]=D[l-1][j];
        }
    }
    P[1]=0;
    for(i=2;i<=k;i++)
        P[i]=P[i/2]+1;
    for(i=1;i<=m;i++)
    {
        fin>>x>>y;
        l=P[y-x+1];
        elem z=minim(D[l][x],D[l][y-(1<<l)+1]);
        fout<<E[z.e].e<<"\n";
    }
    return 0;
}