#include <bits/stdc++.h>
using namespace std;
const int N=500000+5;
struct wer{
	int to,next;
}eg[2*N];
int head[N],ne=1,t[N];
void add(int x,int y){
	eg[++ne]={y,head[x]};
	head[x]=ne;return ;
}
int n,q,lgn;
int vis[N]={0};
bool in[N],huan[N];
int st[N],tp=0,cnt=0,tot=0;
vector<int>v[N],fr[N];
int d[N],c[N],anc[N][30];
int rt[N],hid[N],hpos[N],dir[N];
void dfs(int pt,int lst){
	st[++tp]=pt;vis[pt]=1;
	for (int i=head[pt];i!=0;i=eg[i].next){
		int x=eg[i].to;
		if (i==(lst^1)||vis[x]==2)continue;
		if (vis[x]==1){
			cnt++;
			while(st[tp]!=x){
				v[cnt].push_back(st[tp]);
				vis[st[tp]]=2;huan[st[tp]]=1;tp--;
			}
			v[cnt].push_back(x);huan[x]=1;vis[x]=2;tp--;
			return ;
		}
		if (vis[x]==0) dfs(x,i);
	}
	vis[pt]=2;tp--;
	return ;
}
int dep[N];
void dfs2(int pt,int id,int id2){
	c[pt]=id;d[pt]=id2;
	for (int i=0;i<fr[pt].size();i++){
		int x=fr[pt][i];
		if (huan[x])continue;
		dep[x]=dep[pt]+1;anc[x][0]=pt;
		dfs2(x,id,id2);
	}
	return ;
}
int lca(int a,int b){
	if (dep[a]<dep[b])swap(a,b);
	for (int i=lgn;i>=0;i--){
		if (anc[a][i]!=0&&dep[anc[a][i]]>=dep[b])a=anc[a][i];
		if (a==b)return a;
	}
	for (int i=lgn;i>=0;i--){
		if (anc[a][i]!=anc[b][i]){
			a=anc[a][i];b=anc[b][i];
		}
	}
	return anc[a][0];
}
struct sdf{
	int x,y;
}ans[4];
bool cmp(sdf a,sdf b){
	if (max(a.x,a.y)!=max(b.x,b.y))return max(a.x,a.y)<max(b.x,b.y);
	if (min(a.x,a.y)!=min(b.x,b.y))return min(a.x,a.y)<min(b.x,b.y);
	return a.x>=a.y;
}
int main(){
	freopen ("rdz.in","r",stdin);
	freopen ("rdz.out","w",stdout);
	scanf("%d%d",&n,&q);
	lgn=1.0*log(n)/log(2);
	for (int i=1;i<=n;i++){
		int x;scanf("%d",&x);
		in[x]=1;fr[x].push_back(i);
		add(i,x);add(x,i);t[i]=x;
	}
	for (int i=1;i<=n;i++){
		if (!vis[i])dfs(i,0);
	}
	for (int i=1;i<=cnt;i++){
		for (int j=0;j<v[i].size();j++){
			int x=v[i][j];
			dep[x]=0;dfs2(x,++tot,i);
			hpos[x]=j+1;hid[x]=i;rt[tot]=x;
		}
		if (v[i].size()==1)continue;
		if (t[v[i][1]]==v[i][2])dir[i]=1;
		else dir[i]=2;
	}
	for (int i=1;i<=lgn;i++){
		for (int j=1;j<=n;j++)anc[j][i]=anc[anc[j][i-1]][i-1];
	}
	while(q--){
		int a,b;scanf("%d%d",&a,&b);
		if (d[a]!=d[b]){
			printf("-1 -1\n");continue;
		}
		if (c[a]==c[b]){
			int l=lca(a,b);
			printf("%d %d\n",dep[a]-dep[l],dep[b]-dep[l]);
		}
		else{
			int x=hpos[rt[c[a]]],y=hpos[rt[c[b]]];
			int sz=v[hid[rt[c[a]]]].size();
			int lena=(y-x+sz)%sz,lenb=(x-y+sz)%sz;
			if (dir[hid[rt[c[a]]]]==2)swap(lena,lenb);
			ans[1]={lena+dep[a],dep[b]},ans[2]={dep[a],lenb+dep[b]};
			sort(ans+1,ans+3,cmp);
			printf("%d %d\n",ans[1].x,ans[1].y);
		}
	}
	return 0;
}