#include <fstream>
#include <vector>
#include <queue>
using namespace std;
ifstream f("lca.in");
ofstream g("lca.out");
int father[100005],depth[100005],ind[100005],lg[200005];
pair<int,int> a[20][200005];
vector <int> sons[100005];
vector <int> euler;
queue <int> q;
void parcurgere(int node)
{
    euler.push_back(node);
    ind[node]=euler.size()-1;
    for(auto i:sons[node])
    {
        parcurgere(i);
        euler.push_back(node);
    }
}
int main()
{
    int n,m;
    f>>n>>m;
    for(int i=1;i<n;i++)
    {
        f>>father[i+1];
        sons[father[i+1]].push_back(i+1);
    }
    q.push(1);
    while(!q.empty())
    {
        int x=q.front();
        q.pop();
        for(auto i:sons[x])
        {
            depth[i]=depth[x]+1;
            q.push(i);
        }
    }
    parcurgere(1);
    int l=euler.size();
    lg[2]=1;
    for(int i=3;i<=l;i++)
        lg[i]=lg[i/2]+1;
    for(int i=0;i<l;i++)
        a[0][i]={depth[euler[i]],euler[i]};
    for(int j=1;(1<<j)<l;j++)
        for(int i=0;i+(1<<j)-1<l;i++)
            a[j][i]=min(a[j-1][i+(1<<(j-1))],a[j-1][i]);
    while(m--)
    {
        int aa,bb,x,y;
        f>>aa>>bb;
        x=ind[aa], y=ind[bb];
        pair<int,int> minn={2*n+1,0};
        if(x>y) swap(x,y);
        int k=lg[y-x+1];
        for(int i=k;i>=0;i--)
            if(x+(1<<i)-1<=y)
        {
            minn=min(minn,a[i][x]);
            x+=1<<i;
        }
        g<<minn.second<<'\n';
    }
    return 0;
}