#include<stdio.h>
#include<vector>
using namespace std;
vector <int> g[100005];
int elr[200005],nvl[200005],i,n,k=1,x,m,pp[100005],l,a[20][100005],lg[200005],j,y,ll;


int minn(int a, int b)
{
	if(nvl[a]<nvl[b])return a;
	return b;
}


void ints(int &x,int &y)
{
	if(x>y)
	{
		int aux=x;
		x=y;
		y=aux;
	}
}


void dfs(int lvl, int nod)
{
	int N=g[nod].size();
	for(int i=0;i<N;i++)
	{
		elr[++k]=g[nod][i];
		nvl[k]=lvl;
		dfs(lvl+1,g[nod][i]);
		elr[++k]=nod;
		nvl[k]=lvl-1;
	}
}


int main()
{
	freopen("lca.in","r",stdin);
	freopen("lca.out","w",stdout);
	scanf("%d%d",&n,&m);
	for(i=2;i<=n;i++)
	{
		scanf("%d",&x);
		g[x].push_back(i);
	}
	elr[1]=1;
	dfs(1,1);
	for(i=1;i<=k;i++)
		if(!pp[elr[i]])pp[elr[i]]=i;
	for(i=1;i<=k;i++)
		a[0][i]=i;
	for(i=2;i<=k;i++)
		lg[i]=lg[i/2]+1;
	for(i=1;(1<<i)<=k;i++)
		for(j=1;(1<<i)+j-1<=k;j++)
			a[i][j]=minn(a[i-1][j],a[i-1][(1<<(i-1))+j]);
	for(i=0;i<m;i++)
	{
		scanf("%d%d",&x,&y);
		x=pp[x];
		y=pp[y];
		ints(x,y);
		l=y-x+1;
		ll=lg[l];
		printf("%d\n",elr[minn(a[ll][x],a[ll][y-(1<<ll)+1])]);
	}
	return 0;
}