#include <bits/stdc++.h>
using namespace std;
int n, numQuery, tin[100005], tout[100005], tt, ver[2 * 100005], h[100005],
    p[100005][19];
vector<int> a[100005];
void DFS(int u) {
  tin[u] = ++tt;
  ver[tt] = u;
  for (auto v : a[u]) {
    if (p[u][0] == v) continue;
    h[v] = h[u] + 1;
    p[v][0] = u;
    for (int i = 1; i <= 19 - 1; i++) p[v][i] = p[p[v][i - 1]][i - 1];
    DFS(v);
  }
  tout[u] = ++tt;
  ver[tt] = u;
}
int LCA(int u, int v) {
  if (u == 0) return v;
  if (v == 0) return u;
  if (h[u] > h[v]) swap(u, v);
  int delta = h[v] - h[u];
  for (int i = 0; i <= 19 - 1; i++)
    if ((delta >> i) & 1) v = p[v][i];
  if (u == v) return u;
  for (int i = 19 - 1; i >= 0; i--)
    if (p[u][i] != p[v][i]) {
      u = p[u][i];
      v = p[v][i];
    }
  return p[u][0];
}
struct LCATree {
  int t[100005 << 2];
  void build(int l, int r, int id) {
    if (l == r) {
      t[id] = l;
      return;
    }
    build(l, (r + l) / 2, id * 2);
    build((r + l) / 2 + 1, r, id * 2 + 1);
    t[id] = LCA(t[id * 2], t[id * 2 + 1]);
  }
  int get(int l, int r, int id, int x, int y) {
    if (x > y) return 0;
    if (l > y || r < x) return 0;
    if (l >= x && r <= y) return t[id];
    int a = get(l, (r + l) / 2, id * 2, x, y);
    int b = get((r + l) / 2 + 1, r, id * 2 + 1, x, y);
    return LCA(a, b);
  }
} tLCA;
struct RMQ {
  int Min[100005][19], Mout[100005][19];
  void build() {
    for (int i = 1; i <= n; i++) {
      Min[i][0] = tin[i];
      Mout[i][0] = tout[i];
    }
    for (int i = 1; (1 << i) <= n; i++)
      for (int j = 1; j + (1 << i) - 1 <= n; j++) {
        Min[j][i] = min(Min[j][i - 1], Min[j + (1 << (i - 1))][i - 1]);
        Mout[j][i] = max(Mout[j][i - 1], Mout[j + (1 << (i - 1))][i - 1]);
      }
  }
  int getIn(int l, int r) {
    int k = log2(r - l + 1);
    return ver[min(Min[l][k], Min[r - (1 << k) + 1][k])];
  }
  int getOut(int l, int r) {
    int k = log2(r - l + 1);
    return ver[max(Mout[l][k], Mout[r - (1 << k) + 1][k])];
  }
} rmq;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> numQuery;
  for (int v = 2; v <= n; v++) {
    int u;
    cin >> u;
    a[u].push_back(v);
  }
  DFS(1);
  tLCA.build(1, n, 1);
  rmq.build();
  while (numQuery--) {
    int u, v;
    cin >> u >> v;
    int lef = rmq.getIn(u, v);
    int rig = rmq.getOut(u, v);
    int LCA1 =
        LCA(tLCA.get(1, n, 1, u, lef - 1), tLCA.get(1, n, 1, lef + 1, v));
    int LCA2 =
        LCA(tLCA.get(1, n, 1, u, rig - 1), tLCA.get(1, n, 1, rig + 1, v));
    if (h[LCA1] > h[LCA2])
      cout << lef << ' ' << h[LCA1] << '\n';
    else
      cout << rig << ' ' << h[LCA2] << '\n';
  }
}
