#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 10;
vector<int> G[maxn];
int d[maxn], f[maxn][20], id[maxn], rak[maxn];
int tot = 0;
struct node {
  int mx, mn;
} tr[maxn * 4];
void dfs(int u, int fa, int dep) {
  id[u] = ++tot;
  rak[tot] = u;
  d[u] = dep;
  f[u][0] = fa;
  for (int i = 1; i <= 18; i++) f[u][i] = f[f[u][i - 1]][i - 1];
  for (auto v : G[u])
    if (v != fa) dfs(v, u, dep + 1);
}
int lca(int u, int v) {
  if (d[u] < d[v]) swap(u, v);
  for (int i = 18; i >= 0; i--)
    if (d[f[u][i]] >= d[v]) u = f[u][i];
  if (u == v) return d[u];
  for (int i = 18; i >= 0; i--)
    if (f[u][i] != f[v][i]) u = f[u][i], v = f[v][i];
  return d[f[u][0]];
}
void push_up(int o) {
  tr[o].mx = max(tr[o * 2].mx, tr[o * 2 + 1].mx);
  tr[o].mn = min(tr[o * 2].mn, tr[o * 2 + 1].mn);
}
void build(int o, int l, int r) {
  if (l == r) {
    tr[o].mx = tr[o].mn = id[l];
    return;
  }
  build(o * 2, l, (l + r) / 2);
  build(o * 2 + 1, (l + r) / 2 + 1, r);
  push_up(o);
}
void up(int o, int l, int r, int k, int p) {
  if (l == r) {
    tr[o].mx = tr[o].mn = p;
    return;
  }
  if (k <= (l + r) / 2)
    up(o * 2, l, (l + r) / 2, k, p);
  else
    up(o * 2 + 1, (l + r) / 2 + 1, r, k, p);
  push_up(o);
}
int qu(int o, int l, int r, int ql, int qr, int op) {
  if (ql <= l && qr >= r) {
    if (op == 1)
      return tr[o].mx;
    else
      return tr[o].mn;
  }
  int ans;
  if (op == 1)
    ans = -2e9;
  else
    ans = 2e9;
  if (ql <= (l + r) / 2) {
    if (op == 1)
      ans = max(ans, qu(o * 2, l, (l + r) / 2, ql, qr, op));
    else
      ans = min(ans, qu(o * 2, l, (l + r) / 2, ql, qr, op));
  }
  if (qr > (l + r) / 2) {
    if (op == 1)
      ans = max(ans, qu(o * 2 + 1, (l + r) / 2 + 1, r, ql, qr, op));
    else
      ans = min(ans, qu(o * 2 + 1, (l + r) / 2 + 1, r, ql, qr, op));
  }
  return ans;
}
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  for (int i = 2; i <= n; i++) {
    int u;
    scanf("%d", &u);
    G[i].push_back(u);
    G[u].push_back(i);
  }
  dfs(1, 0, 0);
  build(1, 1, n);
  for (int i = 1; i <= q; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    int x1 = qu(1, 1, n, l, r, 1);
    int y1 = qu(1, 1, n, l, r, 2);
    up(1, 1, n, rak[x1], (int)-2e9);
    int x2 = qu(1, 1, n, l, r, 1);
    up(1, 1, n, rak[x1], x1);
    int x3 = qu(1, 1, n, l, r, 1);
    int y2 = qu(1, 1, n, l, r, 2);
    up(1, 1, n, rak[y2], (int)2e9);
    int y3 = qu(1, 1, n, l, r, 2);
    up(1, 1, n, rak[y2], y2);
    int lca1 = lca(rak[x2], rak[y1]), lca2 = lca(rak[x3], rak[y3]);
    if (lca1 >= lca2)
      printf("%d %d\n", rak[x1], lca1);
    else
      printf("%d %d\n", rak[y2], lca2);
  }
}
